  Polarization sets were introduced by Dencker (1982) as a refinement of
wavefront sets to the vector-valued case. He also clarified the propagation of
polarization sets when the characteristic variety of the pseudodifferential
system under study consists of two hypersurfaces intersecting tangentially
(1992), or transversally (1995). In this paper, we consider the case of more
than two intersecting characteristic hypersurfaces that are interesting
transversally (and we give a note on the tangential case).
  Mainly, we consider two types of systems which we name "systems of
generalized transverse type" and "systems of MHD type", and we show that we can
get a result for the propagation of polarization set similar to Dencker's
result for systems of transverse type. Furthermore, we give an application to
the MHD equations.
