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 $0 \leq v < \infty$. 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.