Born in La Roche-sur-Yon, he helped found a local independent Marxist organisation while still in his teens. Expelled from school, he moved to Paris and became associated with the Trotskyist group around La Verité. In 1930 this group founded the Communist League. This considered itself an external faction of the Communist Party of France, and as such it only admitted current and former PCF members. However, this rule was relaxed and Craipeau was allowed to join in 1931. He joined the League's executive committee with responsibility for developing a youth wing.
By 1933, he was able to organise a meeting attended by one thousand members of the youth wings of the Communist Party and the Section française de l'Internationale ouvrière. During 1933, he was Trotsky's personal secretary.
In 1936, Craipeau became a leading member of the new Internationalist Workers Party (POI). The following year, in reaction to Trotsky's The Revolution Betrayed, he began a re-analysis of the nature of the Soviet Union. He concluded that it could not be defended, as Trotsky held, as a degenerated workers' state, but that it was a bureaucratic collectivist system - an idea he introduced to Trotskyism.
During World War II, he was pronounced unfit for duty, and attempted, with Marcel Hic, to publish La Verité secretly. This was difficult, and following a series of setbacks, he turned instead to work influencing the German Army.
In 1944, Craipeau was the architect of unity between three of France's four Trotskyist groups: the POI itself,the Comités Communistes Internationalistes and the Octobre group. They formed the PCI Internationalist Communist Party, and in 1946, he was elected its General Secretary. In the same year, he was also elevated to the International Secretariat of the Fourth International. However, he could not agree with the International's perspective that a crisis in capitalism was imminent, and soon after the POI sided with the International, he was expelled.
In 1954, Craipeau returned to mainland France, where he participated in the creation of the New Left. This fused with the Movement for the Liberation of the City to form the Socialist Left Union and, in 1960 with several groups to form the Unified Socialist Party. He remained a leading member of this party for many years, during which he wrote numerous books on left-wing politics and revolution.
- Patrick Silberstein, Yvan Craipeau, un "dinosaurio trotskista" (Spanish)
- The 'Third Camp' in France
- Yvan Craipeau Papers
- Mémoires d'un Dinosaure Trotskyste, L'Harmattan, Paris, 1999