The group's origins lie in the
International Committee of the Fourth International (ICFI). Moreno's supporters followed the American
Socialist Workers Party in leaving the ICFI in 1963 to form the
reunified Fourth International (USFI).
 In 1969, the USFI voted to support
guerrilla war in
Latin America. Moreno's group opposed this.
 It was reduced to sympathiser status.
While critical of the
Sandinistas, Moreno's group sent a Simon Bolivar Brigade to
Nicaragua to aid the
 with the aim of building a revolutionary party there. This brigade was opposed by the reunified Fourth International
 because it operated outside the discipline of the
 the only other Trotskyists to participate were
Organising Committee for the Reconstruction of the Fourth International. Forty non-Nicaraguan members of the Brigade were expelled from the country by the FSLN.
 Almost immediately, Moreno's and Lambert's tendencies joined to form the
Parity Committee for the Reconstruction of the Fourth International.
 However, Moreno's supporters withdrew in 1981
 complaining that Lambert had links to
trade union bureaucrats, and in 1982 formed the "International Workers League (Fourth International)". In addition to their former supporters, this also attracted groups in Peru and Venezuela which split from the Lambertist currents.
The group campaigned for the victory of Argentina in the
Falklands War, for the non-payment of
foreign debt, and for the "defeat of
imperialism in the
Gulf War." In the mid-1990s, it helped launch
Workers' Aid to Bosnia and began working with the
Workers International to Rebuild the Fourth International, although that group is now inactive.
Disagreements following the death of Moreno led several sections to leave the international, while others split. Those who left founded the
International Centre of Orthodox Trotskyism (CITO in Spanish). The majority of this group rejoined the International Workers League in 2005, the minority forming the
International Socialist League.
The LITci publishes the bulletin International Courier (Correo Internacional) and the journal
Marxism Alive (Marxismo Vivo or Le Marxisme Vivant), both in various languages, principally