The following paper can be obained from my www page with address http:\\www.ugr.es\~bullejos \title{On the equivariant 2-type of a $G$-space} \begin{abstract} A classical theorem of Mac Lane and Whitehead states that the homotopy type of a topological space with trivial homotopy at dimensions 3 and greater can be re\-con\-struct\-ed from its $\pi_1$ and $\pi_2$, and a cohomology class $k_3\in H^3(\pi_1,\pi_2)$. More recently, Moerdijk and Svensson suggested the possibility of using Bredon cohomology to extend this result to the equivariant case, that is, for spaces $X$ equipped with an action by a fixed group $G$. In this paper we carry out this suggestion and prove an analogue of the classical result in the equivariant case. \end{abstract}