  We present in a local form the time dependent effective description of a
superfluid Fermi liquid which includes Landau damping effects at $T\neq 0$.
This is achieved by the introduction of an additional variable, the
quasiparticle distribution function, which obeys a simple kinetic equation. The
transport equation is coupled with first order equations for the Goldstone mode
and the particle density. We prove that a main feature of this formulation is
its Hamiltonian structure relative to a certain Poisson bracket. We construct
the Hamiltonian to quadratic order.
