  In this paper, we first introduce the notions of superfluous and coessential
subacts. Then hollow and co-uniform S-acts are defined as the acts that all
proper subacts are superfluous and coessential, respectively. Also it is
indicated that the class of hollow S-acts is properly between two classes of
indecomposable and locally cyclic S-acts. Moreover, using the notion of radical
of an S-act as the intersection of all maximal subact, the relations between
hollow and local S-acts are investigated. Ultimately, the notion of a
supplement of a subact is defined to characterize the union of hollow S-act.
