The propagation of Hermite-Gauss beams in absorbing media has been stu
died. The beam attenuation has been demonstrated to increase with the
beam order index. As a consequence, during the propagation in absorbin
g media, the degree of global coherence increases for the whole class
of beams that can be expanded into a series of Hermite-Gauss functions
. Numerical simulations are presented. An application to multimode las
ers is also considered.