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A treatment in a neighborhood and at a point of the equivalence principle onthe basis of derivations of the tensor algebra over a manifold is given.Necessary and sufficient conditions are given for the existence of local bases,called normal frames, in which the components of derivations vanish in aneighborhood or at a point. These frames (bases), if any, are explicitlydescribed and the problem of their holonomicity is considered. In particular,the obtained results concern symmetric as well as nonsymmetric linearconnections.Comment: LaTeX2e, 9 pages, to be published in Journal of Physics A:  Mathematical and Genera

Normal frames and the validity of the equivalence principle: I. Cases in a neighbourhood and at a point