In this paper we present a new set of nonlinear PML equations for the multi-dimensional Maxwells equations and show that they are strongly well posed and temporally stable.The equations are given in vector form and so may be directly written in any ortogonal coordinate system.Another virtue of this set is that there is no need for nonphysical variables in the absorbing layer, thus greatly reducing the number of equations that one solves numerically (6 instead of 12 in the three dimensional case).