  We derive a finite temperature time-dependent effective theory for the phase
$\theta$ of the pairing field, which is appropriate for a 2D conducting
electron system with non-retarded d-wave attraction. As for s-wave pairing the
effective action contains terms with Landau damping, but their structure
appears to be different from the s-wave case due to the fact that the Landau
damping is determined by the quasiparticle group velocity $v_g$, which for the
d-wave pairing does not have the same direction as the non-interacting Fermi
velocity $v_F$. We show that for the d-wave pairing the Landau terms have a
linear low temperature dependence and in contrast to the s-wave case are
important for all finite temperatures.
