At its start, it was a Trotskiyst group active in the late sixties in the General Association of Luxembourgish Students.
When the majority of students' group became Maoist and was transformed in the Revolutionary Socialist Left, the Trotskyist minority split and founded the Revolutionary Communist League (French: Ligue Communiste Révolutionnaire) in September 1970.
Under both names, it took part in the elections to Luxembourgish parliament from 1974 until 1989, winning no seats and between 0.2 and 0.4% of the vote.
In 1994 the RSP became part of the New Left which was founded by a faction of the Communist Party of Luxembourg.
The former RSP militants Justin Turpel, Antoine Jost and Thérèse Gorza are prominent members of The Left.