It was founded as the Movement for a Revolutionary Communist International. Its first member groups were Workers Power (Britain), the Irish Workers Group, Pouvoir Ouvrier in France and Gruppe Arbeitermacht in Germany (GAM). After ArbeiterInnen Standpunkt in Austria joined it became the League for a Revolutionary Communist International (LCRI). This was reportedly not due to any political factor other than the fact that their name in Spanish was very similar to the international tendency of which Sendero Luninoso is a part of. the LRCI was of course in the process of recruiting the Poder Obrero groups of Bolivia and Peru.
The tendency has for many years held that a new international is necessary, and that the fragments of the Fourth International cannot merely be brought together, but the new call for a Fifth International has proven controversial.