A catalyst system for the ring-opening matathesis polymerization, which consists of at least two components (a) and (b), wherein(a) is a ruthenium compound of formula I or IIRuX.sub.2 (L.sub.1).sub.m (L.sub.2).sub.n (L.sub.3).sub.o (L.sub.4).sub.p (I),ARuX.sub.2 (L.sub.1).sub.r L.sub.2).sub.3 (II),wherein L.sub.1,L.sub.2, L.sub.3 and L.sub.4 are each independently of the other C.sub.1 -C.sub.18 alkylcyanide, C.sub.6 -C.sub.24 - aralkylcyanide, tertiary amine, tertiary phosphine which does not contain any secondary alkyl or cycloalkyl radicals bound to the phosphorus atom, or phosphite, X is halogen, A is arene, m, n, o and p are integers from 0 to 4, where 2.ltoreq.m+n+o+p.ltoreq.4, r and s are integers from 0 to 2, where 1.ltoreq.r+s.ltoreq.2, and(b) is a tertiary phosphine containing at least one secondary alkyl radical or cycloalkyl radical bound to the phosphorus atom,is particularly suitable for the polymerisation of strained cycloolefins by the RIM process.