In this paper we continue the study of the characterization of selection principles in the hyper-spaces CL(X), K(X), F(X) and CS(X), endowed with the hit-and-miss topology, by using π ∆ (Λ)-networks and c ∆ (Λ)-covers of a topological space X. Specifically, we prove theorems which characterize the covering properties Hurewicz, strongly star Hurewicz, star Hurewicz and absolutely strongly star Hurewicz in these hyperspaces.