When the Soviet Union invaded east Poland in 1939, many Poles and Jews panicked and fled to the Nazi-occupied west. Nothing, they thought, could be worse than Stalin. At one bridge an SS-officer watched this in disbelief. "Where on earth are you going?" he exclaimed."We are going to kill you."

It wasn't just Poland. Millions of east Europeans were trapped between Germany and the Soviet Union, the two most murderous regimes in European history. Their story is at the heart of Timothy Snyder's outstanding book. What he calls "the Bloodlands", that huge area stretching from the Baltic to the Black Sea, is "where Europe's most murderous regimes did their most murderous work".

For Snyder, this period of violence begins in 1933 not with Hitler's rise to power but with Stalin's decision to starve more than three million Ukrainians to death. Then came the killing of 700,000 Soviet citizens, shot during the Great Terror of 1937-38. At this point, the Soviet Union was "the only state in Europe carrying out policies of mass killing". Before 1939, the Nazi regime "killed no more than ten thousand people. The Stalinist regime had already starved millions and shot the better part of a million."

200,000 Polish citizens were shot by the Soviets or Germans at the beginning of the Second World War. When Germany invaded the Soviet Union in 1941 the atrocities escalated. Four million Soviet citizens were starved to death by the Germans, including three million Soviet prisoners of war. More than five million Jews were gassed or shot by the Germans. In total, Snyder concludes, in the middle of Europe in the middle of the 20th century, the Nazi and Soviet regimes murdered some 14 million people. This doesn't include soldiers killed on the Eastern Front. The Bloodlands were the site of the Nazi death camps, mass shootings by the NKVD and the Einsatzgruppen, campaigns of mass starvation by both the Soviet Union and the Nazis, and the scene of the worst fighting of the war. And it could have been worse. If the Nazis had won, tens of millions of Slavs would have been killed, creating a living space in the east for German colonist-farmers.

We think of the Germans as the main perpetrators. Snyder has none of this. The point is, he argues, that murdering was most intense in the countries which were occupied first by the Soviet Union, then by the Germans and then, again, by the Red Army. That dynamic is crucial. Ukrainians and Latvians welcomed Germans because they couldn't believe anything could be as bad as Stalin. Two inhuman utopian visions clashed and for those caught in between the result was catastrophe.

In addition to the mass killings, there were huge deportations. In Soviet Belarus about two million people were killed, but two million were also deported and a million more fled from the German invasion. "By the end of the war," writes Snyder, "half of the population of Belarus had either been killed or moved." Nor did it stop in 1945. Then came the ethnic cleansing and mass population movements of the post-war years. Snyder takes the story up to Stalin's death in 1953.

Bloodlands is well written, clear and accessible. The book is packed with up to date statistics -- many simply astonishing -- but there are also moving accounts of individuals. Stories like that of Jozef Sobolewski, a toddler, starved to death with his mother and five of his brothers and sisters in 1933 in the Ukraine. The one brother who survived was shot in 1937, in Stalin's Terror.

Some of this is familiar. A great deal, however, isn't. Snyder is a key figure in the new thinking about eastern Europe which is transforming the way we think about Stalinism, Nazism and the Holocaust. Any illusions you might have about the decency of the Wehrmacht or of Stalin's regime will not survive reading this book. We think of German concentration camps and the Gulag as the worst symbols of totalitarianism, but most of those who entered German concentration camps survived. 90 per cent of those who entered the Gulag left it alive. Most of the killings went on in pits, forests, death camps and "starvation zones", some gassed, most shot or starved, in east Europe and the west of the Soviet Union. Not, Snyder is emphatic here, in Russia. But in the non-Russian periphery of the Soviet Union, above all, the Ukraine, Belarus and formerly Soviet-occupied east Poland. Even Stalin's Great Terror was not concentrated in Russia. Of nearly 700,000 executions carried out for political crimes in 1937-38, few were poets or old Bolsheviks. More than 625,000 were kulaks or members of non-Russian minorities.

Snyder has pulled together a huge amount of new thinking and research, much of it not yet translated. It is a formidable work of scholarship, shattering many myths, and opening up a fascinating new history of Europe.

Bloodlands: Europe Between Hitler and Stalin

Timothy Synder

Bodley Head, 544pp, £25