  Following Favre, we define a holomorphic germ f:(C^d,0) -> (C^d,0) to be
rigid if the union of the critical set of all iterates has simple normal
crossing singularities. We give a partial classification of contracting rigid
germs in arbitrary dimensions up to holomorphic conjugacy. Interestingly
enough, we find new resonance phenomena involving the differential of f and its
linear action on the fundamental group of the complement of the critical set.
