Hamilton was for many years closely linked with Gerry Healy but, in 1971, she sided with Pierre Lambert and the French OCI Internationalist Communist Organisation when the ICFI split into two, ostensibly over the place of philosophy in Marxist theory, but equally about control of the ICFI after the OCI grew to be larger than the SLL in the late 1960s.
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The Orthodox Trotskyists suffered another split in 1973 between the Socialist Labour League (SLL) of Gerry Healy and the Internationalist Communist Organisation (OCI) of Pierre Lambert.