  We consider an extension of the zero-range process to the case where the hop
rate depends on the state of both departure and arrival sites. We recover the
misanthrope and the target process as special cases for which the probability
of the steady state factorizes over sites. We discuss conditions which lead to
the condensation of particles and show that although two different hop rates
can lead to the same steady state, they do so with sharply contrasting
dynamics. The first case resembles the dynamics of the zero-range process,
whereas the second case, in which the hop rate increases with the occupation
number of both sites, is similar to instantaneous gelation models. This new
"explosive" condensation reveals surprisingly rich behaviour, in which the
process of condensate's formation goes through a series of collisions between
clusters of particles moving through the system at increasing speed. We perform
a detailed numerical and analytical study of the dynamics of condensation: we
find the speed of the moving clusters, their scattering amplitude, and their
growth time. We finally show that the time to reach steady state decreases with
the size of the system.
