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Abstract. A homotopy action of a group G on a space X is a homomorphism from G to the group of homotopy classes of homotopy equivalences of X. The question studied in this paper is: When is a homotopy action equivalent, in an appropriate sense, to a topological action of G on XI Introduction. A homotopy action of a group G on a space X is a homomorphism a from G to the group &{X) of homotopy classes of homotopy equivalences of X. If G acts on X via homeomorphisms, the associated homotopy action is called topological. A homotopy action a of G on X is equivalent to a homotopy action ß of G on Y if there exists a homotopy equivalence/: X -» Y such that the diagram

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