SKA was formed in 1956 by a small group of stalinist hardliners left or were expelled from SKP during the 50's. This group had earlier formed "marxist circles", in which some SKP militants participated secretly. The group was headed by Set Persson, a famous communist from Stockholm who had left SKP at the party congress in 1953.
SKA started publishing the magazine "Revolt". SKA defended Stalin and criticized the new regime of Chrustjov. They criticized SKP for what they considered as "populism". But the group of Persson also expressed some criticism over the human rights situation within the Socialist Block.
In 1958 SKA tried to launch their own list for the municipal elections in Stockholm, but failed to get any seats. Persson died in 1960. After his death he group almost disappeared but continued to exist until 1967. SKA never played any role in Swedish politics, but the organizational experiences of the people active who were in SKA became important for the later generation of ultraleftists, such as the KFML.