  We develop a theory of conductivity of type-II superconductors in the flux
flow regime taking into account random spatial fluctuations of the system
parameters, such as the gap magnitude $\Delta$(r) and the diffusion coefficient
D(r). We find a contribution to the conductivity that is proportional to the
inelastic relaxation time $\tau_{in}$, which is much longer than the elastic
relaxation time. This new contribution is due to Debye-type relaxation, and it
can be much larger than the conventional flux flow conductivity due to Bardeen
and Stephen. The new contribution is expected to dominate in clean
superconductors at low temperatures and in magnetic fields much smaller than
$H_{c2}$.

Superconductivity