Let φ , φ 1 , φ 2 , … be a sequence of random compact sets on a complete and separable metric space ( S , d ) . We assume that P { φ n ∩ B = ∅ } → P { φ ∩ B = ∅ } for all B in some suitable class B and show that this assumption determines if the sequence { φ n } converges in distribution to φ . This is an extension to general Polish spaces of the weak convergence theory for random closed sets on locally compact Polish spaces found in Norberg [1984. Convergence and existence of random set distributions. Ann. Probab. 12, 726–732.]