This paper is devoted to present some properties of the Baer-invariants of groups with respect to two varieties V and W of groups. We give some inequalities for such Baer-invariants of finite groups. A generalized version of the Stalling type theorem is presented. Also, if N is a normal subgroup of a group G in the variety W, then we give a necessary and sufficient condition for which the Baer-invariant of G can be embedded into the Baer-invariant of the factor group G/N.