A formation [Formula: see text] of finite groups has the generalized Wielandt property for residuals, or [Formula: see text] is a GWP-formation, if the [Formula: see text]-residual of a group generated by two [Formula: see text]-subnormal subgroups is the subgroup generated by their [Formula: see text]-residuals. The main result of this paper describes a large family of GWP-formations to further the transparence of this kind of formations, and it can be regarded as a natural step toward the solution of the classification problem.