ALGEBRAIC CLASSIFICATION OF EQUIVARIANT HOMOTOPY 2-TYPES .1.

We show that the category of diagrams of 2-groupoids indexed by the or bit category O(G) of a group G admits a closed Quillen model structure . The associated homotopy category is then proved to be equivalent to the homotopy category of all G-spaces with the property that the nth h omotopy group of each fixpoint set vanishes for n greater-than-or-equa l-to 3. This result is the equivariant analogue of the classical Mac L ane-Whitehead correspondence between crossed modules and pointed conne cted CW-complexes (X, x0) for which pi(i)(X, x0) = 0 for i greater-tha n-or-equal-to 3.