The class of monotone input/output automata has been shown in the authors' previous work to be a useful operational model for dataflow-style networks of communicating processes. An interesting class of problems arising from this model are those that concern the relationship between the input/output behavior of automata to the structure of their transition graphs. In this paper, we restrict our attention to the subclass of determinate automata, which compute continuous functions, and we characterize classes of determinate automata that compute: (1) the class of functions that are stable in the sense of Berry, and (2) the class of functions that are sequential in the sense of Kahn and Plotkin.