Desertion in war is not a mystery. It can have contributory motives  "family problems" at home, hatred of some officer or moral reluctance to kill are among them. But the central motive is the obvious one: to get away from people who are trying to blow your head off or stick a bayonet through you. Common sense, in other words. So the enigma is not why soldiers desert. It is why most of them don't, even in battle and even in the face of imminent defeat (remember the stubborn Wehrmacht in the second world war). They do not run away, but stand and fight. Why?

That is the most interesting thing in Charles Glass's new book. He takes three young men  boys, really  who were drafted into the infantry in the last European war, who fought, deserted, and yet often fought again. Steve Weiss was from a Jewish family in Brooklyn; his father had been wounded and gassed in the first world war. Alfred Whitehead came from the bleakest rural poverty in Tennessee. John Bain was English (and after the war became famous as the poet Vernon Scannell); he was desperate to get away from his sadistic father, another veteran of the trenches.

All three quit their posts for solid and obvious reasons. Two of them deserted several times over. They saw heartbreaking horrors, or were tempted by women, booze and loot in a liberated city, or were shattered by prolonged artillery barrages, or realised  suddenly, and with cold clarity  that they would almost certainly be killed in the next few days.

The common sense of desertion was plain to almost anyone who had actually been under fire. Again and again, Glass's book tells how these men on the run were fed, sheltered, comforted and transported by soldiers close to the front line. But the further away from the guns they got, entering the reposeful regions of pen-pushing "rear echelons", the more wary, disapproving and uncomprehending their compatriots became. Ultimately they would end up in the hands of the military police, and then in some nightmare "stockade" or military prison where shrieking, muscle-bound monsters who had never been within miles of a mortar "stonk" devoted themselves to breaking their spirit.

Soviet and German treatment of deserters, a story of pitiless savagery, is not mentioned here. Glass is concerned only with the British and Americans in the second world war, whose official attitudes to the problem were tortuous.

In the first world war, the British shot 304 men for desertion or cowardice, only gradually accepting the notion of "shell-shock". In the United States, by contrast, President Woodrow Wilson commuted all such death sentences. In the second world war, the British government stood up to generals who wanted to bring back the firing squad (the Labour government in 1930 had abolished the death penalty for desertion). Cunningly, the War Office suggested that restoration might suggest to the enemy that morale in the armed forces was failing. President Roosevelt, on the other hand, was persuaded in 1943 to suspend "limitations of punishment". In the event, the Americans shot only one deserter, the luckless Private Eddie Slovik, executed in France in January 1945. He was an ex-con who had never even been near the front. Slovik quit when his unit was ordered into action, calculating that a familiar penitentiary cell would be more comfortable than being shot at in a rainy foxhole.

His fate was truly unfair, set against the bigger picture. According to Glass, "nearly 50,000 American and 100,000 British soldiers deserted from the armed forces" during the war. Some 80% of these were front-line troops. Almost all "took a powder" (as they said then) in the European theatres of war; there were practically no desertions from US forces in the Pacific, perhaps because there was nowhere to go. By the end of the conflict, London, Paris and Naples, to name only a few European cities, swarmed with heavily-armed Awol servicemen, many of them recruited into gangs robbing and selling army supplies. Units were diverted from combat to guard supply trains, which were being hijacked all over liberated Europe. Paris, where the police fought nightly gun battles with American bandits, seemed to be a new Chicago.

But none of Glass's three subjects left the front as soon as fighting began. They tried to do their duty for as long as they could. Steve Weiss first encountered battle in Italy, posted to the 36th infantry division near Naples after the Salerno and Anzio landings. He was 18 years old. At Anzio he saw for the first time deserters in a stockade yelling abuse at the army, found that a friend had collapsed with "battle fatigue", and was bombed from the air. 

Soon he was fighting his way up Italy with "Charlie Company", facing artillery and snipers by day and night. Once, exhausted, rain-drenched and on his own, he broke down in tears of fatigue and terror and cried out for his mother. Next day he was street-fighting in the ruins of Grosseto. What kept him going? Not ideals about the war. He had seen Naples, now run by the Mafia boss Vito Genovese in cahoots with the Americans, and the notion that Roosevelt's "Four Freedoms" could matter to starving Italians was a joke. What kept him and the other two going was comradeship: trust in a friend, or in some older and more experienced member of the squad. For Weiss in Italy, it was Corporal Bob Reigle, and later in France, a Captain Binoche in the resistance. For the truculent Alfred Whitehead, who survived Omaha Beach and the murderous battles of the Normandy "Bocage", it was his fellow-Tennessean Paul "Timmiehaw" Turner; staying drunk helped too. For John Bain, with the 51st Highland Division in North Africa and Normandy, it was his foul-mouthed, loyal pal Hughie from Glasgow.

The war was crazy, the army was brainless and callous, but there were these men who would never let you down, and for whose sake you bore the unbearable. When Weiss rejoined his company in the Vosges and found how many comrades were dead, when "Timmiehaw" was killed by a mine near St-Lo and Hughie by a mortar barrage near Caen, the psychic exhaustion all three young men had been suppressing finally kicked in.

Whitehead left to become a gangster in liberated Paris. Weiss and a few mates ran away from the winter battles in the Vosges hills; he did time in a military prison and eventually became a psychiatrist in California. Bain had already deserted once before, in Tunisia, and served a sentence in the appalling Mustafa Barracks "glasshouse" near Alexandria. Badly wounded in Normandy, he deserted again after the war was over because he couldn't wait to be demobbed, and vanished into London to become poet and boxer Scannell.

Not much of this book, it should be said, is about deserting. Most of it consists of the three men's own narratives of "their war", published or unpublished, and  because they are the stories of individual human beings who eventually cracked under the strain of hardly imaginable fear and misery  they are wonderful, unforgettable acts of witness, something salvaged from a time already sinking into the black mud of the past. I'll certainly remember Bain watching his mates rifling the pockets of their own dead, Weiss witnessing the botched hanging of black soldiers for rape, Whitehead hijacking an American supply truck in the middle of the Paris traffic.

Memorable, too, is the astonishing Psychology for the Fighting Man, a work of startling empathy and humanity, produced in 1943 and distributed to American forces. Glass posts extracts at the outset of each chapter. "Giving up is nature's way of protecting the organism against too much pain." Or "There are a few men in every army who know no fear  just a few. But these men are not normal." Statements of the obvious? Maybe. But in the madness of war, the right to state the obvious becomes worth fighting for.

 Neal Ascherson's Black Sea is published by Vintage.