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In this paper we continue our study of local rigidity for maps of CRsubmanifolds of the complex space. We provide a linear sufficient condition forlocal rigidity of finitely nondegenerate maps between minimal CR manifolds.Furthermore, we show higher order infinitesimal conditions can be used to givea characterization of local rigidity.

Sufficient and necessary conditions for local rigidity of CR mappings and higher order infinitesimal deformations