The current article considers some infinite groups whose finitely generated subgroups are either permutable or pronormal. A group G is called a generalized radical, if G has an ascending series whose factors are locally nilpotent or locally finite. The class of locally generalized radical groups is quite wide. For instance, it includes all locally finite, locally soluble, and almost locally soluble groups. The main result of this paper is the following Theorem. Let G be a locally generalized radical group whose finitely generated subgroups are either pronormal or permutable. If G is non-periodic then every subgroup of G is permutable.