  Recently, [3], it was shown that Special Relativity is in fact based on one
single physical axiom which is that of Reciprocity. Originally, Einstein, [1],
established Special Relativity on two physical axioms, namely, the Galilean
Relativity and the Constancy of the Speed of Light in inertial reference
frames. Soon after, [4,5], it was shown that the Galilean Relativity alone is
sufficient for Special Relativity. Here it is important to note that,
implicitly, three more assumptions have been used on space-time coordinate
transformations, namely, the homogeneity of space-time, the isotropy of space,
and a mathematical condition of smoothness type. In [3], a boundedness
condition on space-time coordinate transformations is used instead of a usual
mathematical smoothness type condition. In this paper it is shown that the
respective boundedness condition is closely related to a Principle of
Transformation Increment Ratio Limitation, or in short, PTIRL, which has an
obvious physical meaning. It is also shown that PTIRL is {\it not} a stronger
assumption than that of the mentioned boundedness in [3]. Of interest is the
fact that, by formulating PTIRL as a physical axiom, the possibility is opened
up for the acceptance, or on the contrary, rejection of this physical axiom
PTIRL, thus leading to {\it two} possible theories of Special Relativity. And
to add further likelihood to such a possibility, the rejection of PTIRL leads
easily to effects which involve unlimited time and/or space intervals, thus are
not accessible to usual experimentation for the verification of their validity,
or otherwise.
