  We examine the effect of spatial correlations on the phenomenon of real-space
condensation in driven mass-transport systems. We suggest that in a broad class
of models with a spatially correlated steady state, the condensate drifts with
a non-vanishing velocity. We present a robust mechanism leading to this
condensate drift. This is done within the framework of a generalized zero-range
process (ZRP) in which, unlike the usual ZRP, the steady state is not a product
measure. The validity of the mechanism in other mass-transport models is
discussed.
