In this work, we introduce the concept of fully pseudo-stable gamma acts as a generalization of fully stable gamma acts. We investigate various properties and characterizations of this class. In particular, we show that an MГ – act A is fully pseudo-stable if and only if every cyclic MГ – subact of A satisfies Baer’s MГ – criterion. Finally, we propose a further generalization, called essentially fully pseudo-stable, which is a very widely occurring property in any MГ – act.