LetA, Bbe associative rings with identity, and (S, ≤) a strictly totally ordered commutative monoid which is also artinian. For any bimoduleAMB, we construct a bimoduleA[[S]]M[S]B[[S]]and prove thatAMBdefines a quasi-duality if and only if the bimoduleA[[S]]M[S]B[[S]]defines a quasi-duality. As a corollary, it is shown that if a ringAhas a quasi-duality then the ringA[[S]] of generalized power series overAhas a quasi-duality.