In this review, we analyze some of the most important theoretical attempts to challenge the invariance of the light speed postulated by the Special Theory of Relativity (STR). Most of those studies, however, show that STR has great stability with respect to various kinds of modi cations in its axioms. This stability probably is due to the fact that in these modi cations there is no so much a violation of the physical postulate of the invariance of the speed of light, as its mathematical expansion in the form of making resort to a more general a ne space. In these modi cations, we refer to more general transformation groups, including scale transformation of the speed of light and timeProducción Científica de la Universidad Autónoma de Zacatecas UAZ