In this paper, we introduce the notions of almost π ∆ (Λ)-network and weakly π ∆ (Λ)-network to characterize the properties of almost Rothberger (Menger) and weakly Rothberger (Menger), respectively, in the hyperspaces CL(X), K(X), F(X) and CS(X), endowed with the hit-and-miss topology. Also, we introduce the concepts of groupable c ∆ (Λ)-cover and weakly (∆, Λ)-groupable cover of X to give equivalences of the selection principles S 1 (D, D p), S fin (D, D p), S 1 (D, D wp) and S fin (D, D wp) in the same hyperspaces.