  A simplified version of the Wigner--transformed time--dependent
Hartree--Fock--Bogoliubov equations, leading to a solvable model for finite
systems of fermions with pairing correlations, is introduced. In this model,
pairing correlations result in a coupling of the Vlasov--type equation for the
normal phase--space density with that for the imaginary part of the anomalous
density. The effect of pairing correlations on the linear response of the
system is studied for a finite one--dimensional system and an explicit
expression for the correlated propagator is given.
