The group played together for 55 years, until 1938. Arnold Rosé was the first violin for the whole of that time, but the other members changed. Julius Egghard played the second violin at first; then it was Albert Bachrich, until 1905 when Paul Fischer joined. The viola player was Anton Loh, then Hugo von Steiner until 1901, then Anton Ruzitska; after 1920, Max Handl played the viola. Eduard Rosé, Arnold’s brother, was the cellist at first, but left after one season he left to get married and was replaced by Reinhold Hummer. The next cellist was Friedrich Buxbaum; cellist Anton Walter joined in 1921, but later on Buxbaum took over once more.
The group were particularly famous between 1905 and 1920, with Rosé, Fischer, Ruzitska, and Buxbaum. They were known for their great performances of Haydn, Mozart and Beethoven, but also some more modern composers including Arnold Schoenberg.
The group often gave the first Vienna performances of works by Brahms, including his Clarinet Quintet and his Quintet in G major Opus 111. It also gave the first performance of Schoenberg's first and second string quartets and the sextet Verklärte Nacht in which they were joined by two other members of the Vienna Philharmonic Orchestra: Franz Jelinek, viola, and Franz Schmidt, cello.