The Ginzburg-Landau effective theory provides a very successful 
phenomenological description of a large class of static superconducting
phenomena,and its form was established by Gorkov soon after the advent of BCS 
theory.The static G-L theory is formally the same as a non-linear 
Schrodinger theory,and it seems natural to suppose that the time-
dependent version of that theory should be the effective G-L theory for the 
non-static case.But this turns out to be by no means obvious-if indeed 
it is true at all.At zero temperature,the expected time-dependent non-linear
Schrodinger theory has only recently been established (I.J.R.
Aitchison, Ping Ao, David J. Thouless, and X.-M. Zhu, Phys.Rev.B 51,
6531 (1995)).At finite temperature,"Landau damping" processes appear 
to preclude {\em any} local effective Lagrangian for non-static processes.
We are pursuing a programme of trying to see under what, if any, 
circumstances a local time-dependent effective theory is nevertheless 
a good approximation. We made the first  
explicit calculation of the Landau damping terms  
in I.J.R.Aitchison and D.J.Lee, Phys.Rev.B 56,8303 (1997). This work 
had limitations: only quadratic fluctuations of the pair field away 
from the zero-temperature value were considered, and the analytic 
properties of the phase field (Goldstone mode) propagator were 
incorrectly represented. These shortcomings have been 
removed in I.J.R.Aitchison, G.Metikas and D.J.Lee, Phys.Rev. B 62, II 
6638-6649 (2000). We show that the retarded Goldstone 
propagator can be well represented by two poles in the lower half 
frequency plane, and we predict the temperature, frequency and 
momentum dependence of the associated damping. We also argue that 
the real parts of the Landau terms contribute to the normal fluid (rather 
than superfluid) component.