The paper develops the mathematical foundations for a parallel recursive estimator for the identification of dynamic parameters for a general n-link high performance robot. The estimation is structured so that one estimator is assigned to each link. Only composite parameters used for calculating joint torques (the inverse dynamic equations) are identified. The parallel structure makes possible the real-time estimation of dynamic parameters, including load and frictions, using only medium-speed processors. A companion paper will verify the performance of the estimator as part of a real-time control structure.