  We investigate properties of stationary aligned and unaligned spiral
perturbation configurations in a composite system of gravitationally coupled
stellar and gaseous singular isothermal disks (SIDs) using the two-fluid
formalism. We obtain stationary perturbation solutions for aligned and
unaligned spiral logarithmic configurations in such a composite SID system and
derive analytically existence criteria for these solutions. In comparison with
the similar problem of a single SID studied by Shu et al. (2000), there are now
two possible sets of solutions owing to an additional SID.
