Abstract. By using purely algebraic methods of n-foldČech derived functors, the higher equivariant integral group homology is investigated from the Hopf formulas point of view.The study of group actions on algebraic objects has many important applications in homotopy theory and K-theory (see for instance [3,10,13,15]). In [11] the first author introduced and studied a natural equivariant version of the classical Eilenberg-Mac Lane (co)homology theory of groups, which can be considered as a part of relative homological algebra. The cohomological characterization of equivariant extensions with operators that are splitting with respect to group actions has motivated the development of this theory, which differs from the (co)homology theory of groups with operators developed in [5,6] motivated by the classification problem of graded categorical groups. Analogues of much of the theory of the classical homological algebra of groups have been obtained in that equivariant setting such as (co)chain and cotriple presentations, the Hopf formula, exact (co)homology sequences, and the Tate cohomology of groups. Moreover, the relationship with the equivariant cohomology of spaces was established, and it was shown that the well known isomorphism of Milnor's K-group K 2 (A) with the second integral homology H 2 (E(A)) of the elementary group E(A) of a unital ring A remains true for arbitrary rings by taking into account the action on E(A) of the Steinberg group St(Z) of the ring Z of integers (see [11, Corollary 24]).As promised we continue the investigation of equivariant homology theory of H. Inassaridze [11]. Namely, using the purely algebraic method of n-foldČech derived functors developed in [7,12], we provide higher Hopf type formulas for the equivariant integral group homology (Theorem 12), extending the Hopf formula for the second equivariant homology [11] and recovering the Brown-Ellis higher Hopf formulas [2], when the group actions are trivial.We set up the following notation. Throughout Γ is a fixed group. G Γ denotes the category of Γ-groups whose objects are groups enriched with a (left) Γ-action and morphisms are Γ-equivariant group homomorphisms, or Γ-homomorphisms for