  We extend the classical notion of a Reedy category so as to allow non-trivial
automorphisms. Our extension includes many important examples occuring in
topology such as Segal's category Gamma, or the total category of a crossed
simplicial group such as Connes' cyclic category Lambda. For any generalized
Reedy category R and any cofibrantly generated model category E, the functor
category E^R is shown to carry a canonical model structure of Reedy type.
