Random sets considered in this paper are random closed sets on Euclidean spaces or more generally, on Hausdorff, Second countable, Locally Compact spaces (HSLC) in the sense of Matheron [11]. As random elements, probability laws of random closed sets are probability measures on the Borel σ-field (generated by the hit-or-miss topology) of subsets of the space of closed sets of a HSLC space. Since this space is metrizable (and compact), the convergence in distribution of sequences of random closed sets can be formally studied in the lines of weak convergence of probability measures on metric spaces (Billingsley [1]). However, due to the complexity of the spaces of sets, one would like to be able to study this type of convergence at some simpler level. This is indeed possible, thanks to Choquet’s theorem (Choquet [2]) characterizing probability laws of random closed sets in terms of their corresponding capacity functionals. In other words, it is possible to study the convergence in distribution of random closed sets by looking at the convergence of capacity functionals as set-functions. This was done by several authors, including Norberg [13, 14], Salinetti and Wets [15], Vervaat [17] and Molchanov [12]. Here, we investigate the convergence in distribution of random closed sets also by looking at their capacity functionals, but from a different point of view. We regard capacity functionals are generalizations of probability measures, and as such, we first define a generalized weak convergence type for them, called Choquet weak convergence, in which ordinary Lebesgue integral (of continuous and bounded functions) with respect to probability measures is replaced by an integral with respect to non-additive set—functions, namely Choquet integral. We then next investigate conditions on this type of Choquet weak convergence of capacity functionals in order to obtain the convergence in distribution of underlying random closed sets.