  We ask what happens when two systems having a nonequilibrium steady state are
kept in contact and allowed to exchange a quantity, say mass, which is
conserved in the combined system. Will the systems eventually evolve to a new
stationary state where certain intensive thermodynamic variable, like
equilibrium chemical potential, equalizes following zeroth law of
thermodynamics and, if so, under what conditions is it possible? We argue that
the zeroth law would hold, provided both systems have short-ranged spatial
correlations and they {\it interact weakly} to exchange mass with rates
satisfying a balance condition - reminiscent of detailed balance in
equilibrium. This proposition is proved for driven systems in general in the
limit of small exchange rates (i.e., weak interaction) and is demonstrated} in
various conserved-mass transport processes having nonzero spatial correlations.
