By 1957, Alexander was already radicalised and a member of the Cape Peninsula Students' Union, an affiliate of The Non-European Unity Movement of South Africa. He joined the African Peoples Democratic Union of Southern Africa (APDUSA) which was established in 1960. However he was ejected from APDUSA in 1961 and with Dulcie September, Ottilie Abrahams, and Andreas Shipinga, among others, formed a study group of nine members in July 1962, known as the Yu Chi Chan Club (YCCC); Yu Chi Chan is the Chinese name for guerrilla warfare, which Mao Zedong used. The YCCC disbanded in late 1962 and was replaced by the National Liberation Front (NLF), which Alexander co-founded. In July 1963, he, along with most members of the NLF, was arrested. In 1964, he was convicted of conspiracy to commit sabotage. From 1964–1974 he was imprisoned on Robben Island