We continue our study of set-valued random processes initiated e.g. in [Proc. Indian Acad. Sci., Math. Sci. 101, No. 2, 63-70 (1991; Zbl 0756.28007)]. In this and other works, we concentrated our attention primarily to set-valued martingales and semi-martingales (i.e., set-valued submartingales and supermartingales). Here we consider two broader classes of set-valued random processes, namely set-valued amarts and uniform amarts.