  We investigate the impact of nonlocality, owing to diffusive behavior, on
transverse instabilities of a dark stripe propagating in a defocusing cubic
medium. The nonlocal response turns out to have a strongly stabilizing effect
both in the case of a single soliton input and in the regime where dispersive
shock waves develop "multisoliton regime". Such conclusions are supported by
the linear stability analysis and numerical simulation of the propagation.
