Recently, the set-valued uncertain process has been introduced that is a sequence of uncertain sets evolving as time goes ahead. The concepts of convergence of set-valued uncertain processes were also defined from different points of view. Here, we elaborate on these definitions and investigate the relationship between them. We prove that some convergence concepts imply others while the inverse is not generally valid. We also propose a novel measure of convergence and verify its relationship with the others. Each finding is described with simple illustrative examples.