  The equations of motion of pair-like excitations in the superconducting state
are studied for various types of pairing using the random phase approximation.
The collective modes are computed of a layered electron gas described by a
$t-t'$ tight-binding band, where the electrons experience besides the
long-range Coulomb repulsion an on-site Hubbard U repulsion and a
nearest-neighbour attractive interaction. {}From numerical calculations we see,
that the collective mode spectrum now becomes particularly rich. Several
branches can occur below the continuum of quasi-particle excitations,
corresponding to order-parameter fluctuations of various symmetries of pairing,
and collective spin-density fluctuations. {}From the collective mode softening
near the nesting vectors it is concluded, that in the d-wave paired state an
instability occurs toward the formation of a spin-density wave.
