Abstract. Collective flows of protons and negative pions have been studied in 2 H+C, Ta and He+C, Ta collisions at energy of 3.4 GeV/nucleon. The data has been obtained by 2m Propane Bubble Chamber (PBC-500) at JINR. It is found that the directed flow of protons and π − -mesons characterized by d< P x >/d(y) increases with increase of the mass numbers of colliding nucleus pairs; the elliptic proton flow points out of the reaction plane and also strengthens as system mass increases; the negative pion directed flow is in the reaction plane as proton one for the lighter ( 2 H+C, He+C) systems and in the opposite direction for the heavier ( 2 H+Ta, He+Ta) systems. In 2 H+C, He+C, C+C, C+Ne, 2 H+Ta, He+Ta, C+Cu and C+Ta collisions, the linear dependence of directed and elliptic flow parameters from mass numbers of projectile and target nuclei ─ (A P . A T ) 1/2 , is similar for protons while for π − -mesons the dependence of directed flow parameters is stronger. The Ultra-relativistic Quantum Molecular Dynamical Model (UrQMD) enlarged by the Statistical Multi-fragmentation Model (SMM) satisfactorily describes the obtained experimental results for all pairs of nuclei. The data for such asymmetric nuclear collisions are obtained for the first time.