Representing the relativistic physical fields as sections of the Clifford Bundle (or of the Spin-Clifford Bundle) of Minkowski spacetime we show that all the relativistic wave equations satisfied by these fields possess solutions traveling with arbitrary speeds 0 < V < OO. By giving rigorous mathematical definitions of reference frames and of the Principle of Relativity (PR) we prove that physical realizations of the V > 1 solutions of, e.g., the Maxwell equations imply in a breakdown of the PR, but in no contradiction at all with known physical facts.where J is the bilateral ideal in TV generated by elements of the form u υ + ν <8> u,u,v G V. The elements of f\V will be called multivectors, or multiforms if they arc elements of f \V*.

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