In 1992, the cryptographic hash function RIPEMD, a European proposal, was introduced as an improved variant of the MD4 hash function. RIPEMD involves two parallel lines of modified versions of the MD4 compression function. Three years later, an attack against a reduced version of RIPEMD in which the first or the last round of the RIPEMD compression function is omitted was described by Hans Dobbertin, who also published in 1998 a cryptanalysis of MD4. In this paper, we present a method for finding collisions in each of the parallel lines of RIPEMD. The collision search procedure requires only a few seconds computing time. We show that although the modifications of the MD4 compression function Used in RIPEMD introduce additional constraints in the cryptanalysis as Compared with Dobbertin’s attack of MD4, these modifications do not result in an increase of the collision search computation time. It is still an open question whether collisions can be found for the full RIPEMD function.