Initially known as Communist Movement M-L (Kommúnistahreyfingin M-L; KHML), from 1972 until 1976 Kommúnistasamtökin marxistarnir-lenínistarnir (KSML).
Chairman was Gunnar Andrésson and General Secretary Kristján Guðlaugsson.
It recognized the Albanian Party of Labor as the leader of the world communist movement.
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