Such is Aleksandar Hemon's bountiful gift for language that the Bosnian-American writer has drawn comparison with Nabokov, that genius of word selection. Both novelists began writing in English relatively late, after first establishing themselves in their native tongues. But as Hemon has noted himself, it's not this linguistic feat that most unites the two writers. Rather it's a sensibility  at once mordant and exuberant, comic and subtle  that Hemon traces to a distinctive Slavic outlook.

The Bosnian has said that he writes "sad books for humorous people" and "humorous books for sad people". The Book of My Lives is a thoughtfully humorous and profoundly sad memoir-cum-collection of essays that explores Hemon's first life, growing up in the lively cultural atmosphere of Sarajevo before the onset of the war in Bosnia, and his second life as a sort of accidental exile in America, where he was effectively trapped in 1992 when the war broke out.

Hemon does with Sarajevo what Orhan Pamuk has done for Istanbul, which is to say he brings to life a city in ways that have little to do with its received image. The tragic story of Sarajevo, particularly the siege by Serbian forces, is one that is familiar from television news reports. Although Hemon takes us through the brute madness of the siege, his Sarajevan streets are populated not with faceless victims but people with plans and ideas and dogs, all of which Hemon has the novelist's ability to make vital.

Perhaps the most disturbing chapter in this section concerns Hemon's former poetry professor, Nikola Koljevic, an enormously learned figure  "with the long, slender fingers of a piano player"  whom the aspiring writer greatly admired. Koljevic could quote Shakespeare in English and seemed to Hemon the very embodiment of high culture.

Yet when Radovan Karadzic began whipping up sectarian hatred, and preparing the destruction of Sarajevo, it was Professor Koljevic who sat encouragingly by his side at press conferences. Hemon does not overplay the dreadful irony of the aesthete turned warmonger. That's not his style. Instead he captures the disjunction perfectly in a deadpan last line about the professor's later suicide: "He had to shoot twice, his long piano-player finger apparently having trembled on the unwieldy trigger."

This is typical Hemon, an expert in subversive deflation. His beautifully assembled vignettes are often digressive but they invariably come back to a particular point and it's usually not the point that you were expecting. Because Hemon, who witnessed the wilful ruination of his famously civilised hometown, knows that life doesn't proceed in straight narrative lines.

Never was this truth more harrowingly confirmed than in the final chapter of the book, which records the death of his infant daughter, Isabel, following the removal of a brain tumour. It's an astonishing piece of writing, and it's hard to imagine that any parent has ever dealt more powerfully or affectingly with the end of his child's life. Hemon retains an unblinking eye for the telling detail in circumstances in which most people would struggle to look at the world at all. Nor does he allow himself or the reader the indulgence of sentimentality, even as he describes the childish coping mechanism of his other daughter's imaginary friend, which he realises is the same process he employs as a novelist "to understand what was hard for me to understand".

As he notes, the ready platitude for such nightmare scenarios is that words fail us. But words did not fail Hemon. Like Nabokov, he is a writer who knows how to make words succeed in the most unpromising places.

Aleksandar Hemon's new book is being billed as his third continuous prose narrative, a non-fiction successor to the novels Nowhere Man and The Lazarus Project, but it has far more in common with Love and Obstacles, a collection of autobiographical narratives linked by their subject  a Bosnian writer who moves to Chicago. Where that exercise, presented as fiction, was streamlined and cumulative, this one, presented as non-fiction, is inscrutable and chaotic. Imagine a jigsaw puzzle with a thousand pieces but no pattern, and you begin to understand this book's awesome powers of frustration.

A "Table of Discontents"  printed at the back  explains that all but one of the chapters have appeared before. (He also admits, in the book's inauspicious opening words, that he has to be "pressed" into writing non-fiction.) There are accomplished memoirs that were assembled in roughly this way, such as Updike's Self-Consciousness and Roger Angell's Let Me Finish, but either with the help of planning in advance or in retrospect, or both. Reading The Book of My Lives, it quickly becomes evident that the component parts, some of them very small and many of them idling, weren't conceived to go together and haven't received much retooling for the purpose. (The only chapter constructed from two pieces is simply a chapter in two parts  the division is marked with a numeral.)

A notable product of Hemon's casual approach is the dearth of basic information. Journalistic writing, even of a personal nature, can get by without the kind of facts we expect in the early stages of a book. You can write articles about chess, football or dogs without letting slip your employment circumstances or marital status, but over the long haul (his first wife is introduced on page 171) the reader is liable to make assumptions.

Hemon's title tries to turn the book's lack of unity into a strength and even a theme  he has been at different points a teenage scallywag and a cautious immigrant, an accidental agitator and a conscious radical, a Sarajevan and a Chicagoan. But if the reference to "lives"  Hemon also describes himself as a "cluster of others"  captures some of his book's eventfulness, it also draws attention to the hole at its centre.

The Hemon depicted here emerges as a magnet for incident and misfortune, but rarely as an agent and never as a self. Ordinary human suffering is next to nonexistent: the threat posed by the birth of a younger sister is told as comedy ("Never again would I have all the chocolate for myself"); life in the Yugoslav People's Army was tough because of the "fantastically limited" menu; a reference to a therapist who helped him with his anger comes out of nowhere only to return there. For a book written by the person it concerns, The Book of My Lives contains unusually few reflections from within  as distinct from essayistic dwelling and digression on themes thrown up by personal experience, such as collective identity, the subject of the trenchant but essentially autonomous opening chapter.

While the book has too little of some things, it has too much of others. On page 66, Hemon recalls that in July 1991, he took a trip to Ukraine, "just in time" for "the collapse of the USSR" and "the subsequent Ukrainian independence", and returned home, to Sarajevo, to find a deflated city and many of his old acquaintances "drugged to the brim". Three pages later, in another chapter, we read: "Much of the summer of 1991, I'd spent in Ukraine, witnessing the demise of the Soviet Union and Ukraine's independence. When I returned to Sarajevo at the end of August, the war had already settled in people's minds: fear, confusion, and drugs reigned." Later still, Hemon writes, casual as you like: "In the summer of 1991, incidents in the neighbouring Croatia developed into a full-fledged fast-spreading war " A detail further down the page muddies the picture of the role played by drugs (was it to aid denial or dull acceptance?): "In the summer of 1991, parties, sex, and drugs were abundant  By September, however, the complicated operations of denial were hopelessly winding down." A story of exile might easily return to a single moment  in this case, the moment that marked the end of the old life. But repetition makes a heavier sound than echo, and no reader is deaf to the difference.

Most of the time, any possibility of development or momentum is scuppered by Hemon's complacency  his failure, or refusal, to smooth transitions and paper over cracks. Radovan Karadzic is introduced as "the talentless poet destined to become one of the world's most wanted war criminals" long after his first appearance (and dismissal as "a minor poet"). A description of Karadzic "flanked by my former professor", initially bemusing, works to ruin the suspense of the later chapter devoted to this man's mutation from devotee of New Criticism to agent of Serbian fascism. Such over-recurring characters only draw attention to the absence of direct engagement with the Bosnian conflict. The chapter that ends "now we were all waiting to see who would live, who would kill and who would die" is followed by one that begins "My family used to have a cabin on the mountain called Jahorina".

Even the book's remarkable closing passages, in which Hemon describes the death of his younger daughter Isabel, are blunted by context. The essay, originally published in 2011, is a howl of pain and grief, utterly ill-suited to round off a collection of journalism so full of emotional deflection. Part of the difficulty is that Hemon is detailing an event that occurred after the writing of almost every other chapter; a series of articles recording a period  from 1992 until 2010  in which Hemon believed that the destruction of his homeland would be the greatest disaster of his adult life are being offered as a single statement at a time when he knows that it hasn't been. The result is that, in light of the ending, much of the book looks curiously out of date. Phrases such as "the loss of our previous life" and "before everything collapsed" might have been reserved for this later rupture; ruined Sarajevo and welcoming Chicago, two of Hemon's main subjects, must look different in the wake of Isabel's death. It is odd and sad that Hemon chose not to acknowledge this shift in his perspective, and settled for compiling a memoir rather than composing one.