In this work we shall show that the transversal magnetic (TM) or transversal electric (TE) electromagnetic evanescent waves have not independent existence: under Lorentz transformations an original TM or TE mode is transformed in a mixture of TM and TE modes out of phase in 7:/2. Through the well-known TORALDO DI FRANCIA expansion of the field of an uniformly moving charge in evanescent waves, we axe able to give a physical reason for this result. An interesting feature of these transformations is that there exist two linear combinations of TM and TE modes (the left- and right-handed circularly polarized modes) which remain the same in all systems. These modes, which propagates with a mean velocity of energy transport equal to c, have an interesting property concerning their helicities which has been recently discussed in the literature.