In this paper, we examine the interior transmission problem for Maxwells equations in the case where both and , the physical parameters of the scattering medium, differ from 0 and 0 modelling the background medium. Using the T-coercivity method, we propose an alternative approach to the classical techniques to prove that this problem is of Fredholm type and that the so-called transmission eigenvalues form at most a discrete set. The T-coercivity approach allows us to deal with cases where 0 and 0 can change sign. We also provide results of localization and FaberKrahn-type inequalities for the transmission eigenvalues. © 2012 IOP Publishing Ltd.