We study S − R‐bimodules SMR with the annihilator condition S = lS(A) + lS(B) for any closed submodule A, and a complement B of A, in MR. Such annihilator condition has a direct connection with the CS‐condition for MR. We make use of this to give a new characterization of CS‐modules. Bimodules SMR for which rMlS(A) = A (for every closed submodule A of MR) are also dealt with. Such modules are called W∗‐modules. We give the extra added annihilator conditions to W∗‐modules to be equivalent to the continuous (quasicontinuous) modules.