The viscous motion of an interface driven non-adiabatically by an ac
external field of frequency omega_0 in a random medium is considered.
The velocity exhibits a smeared depinning transition showing a double hysteresis
in the case when the amplitude of the external field is larger than the
depinning field. This hysteresis is absent in the adiabatic case
omega_0 to 0.
Using scaling arguments and an approximate renormalization group calculation
we explain the main characteristics of the hysteresis loop . In
the low frequency limit these can be expressed in terms of the depinning
threshold and the critical exponents of the adiabatic case.
We use these results to explain experimental measurements of the domain
wall motion in granular >superferromagnetic materials.
We calculate the complex susceptibilities
numerically, and compare the Cole-Cole representations .
 A. Glatz, T. Nattermann, and V. L. Pokrovsky, Phys. Rev. Lett. 90,
 O. Petracic et al., J. Mag. Magn. Mat. 272, E1201 (2004).