We give necessary and sufficient conditions under which a C 0 -semigroup of bi-contractions on a Krein space is similar to a semigroup of contractions on a Hilbert space. Under these and additional conditions we obtain direct sum decompositions of the Krein space into invariant regular subspaces and we describe the behavior of the semigroup on each of these summands. In the last section we give sufficient conditions for the co-generator of the semigroup to be power bounded. r 2004 Elsevier Inc. All rights reserved. MSC: primary 47D60; 47B50; secondary 47A20; 47A15