Block copolymers that have both adsorbing and nonadsorbing blocks can be used to stabilize colloidal dispersions. However, they can also induce an attraction between two particles by forming bridges between the surfaces. In this paper we investigate when such an attraction occurs and how its magnitude depends on the relevant system parameters. Most attention is paid to end-adsorbed triblock (A-B-A) copolymers and a few calculations are presented for polymers consisting of a larger number of blocks ((A-B)n-A with n > 1). Adsorbed layers of triblock copolymers with identical adsorbing groups always cause an attractive part in the two-particle interaction curves. Adsorbed layers of multiblock (n > 1) copolymers with long blocks behave similar to triblock copolymers. When their blocks become very short, these multiblock copolymers resemble homopolymers whose interaction parameters have some average value of those for both types of blocks.