Introduction: The dynamics in systems ranging from intercellular gene regulation to organogenesis are driven by complex interactions (represented as edges) in subcomponents (represented as nodes) in networks. For example, models of coupled switches have been applied to model systems such as neuronal synapses and gene regulatory networks. Similarly, models of coupled oscillators along networks have been used to model synchronization of oscillators which has been observed in synthetic oscillatory fluorescent bacteria, yeast gene regulatory networks, and human cell fate decisions. Moreover, several studies have inferred that biochemical systems contain "network motifs" with both oscillatory and switch-like dynamics. The dynamics of these motifs have been used to model yeast cell cycle regulation and have been further confirmed in synthetic, designed biochemical circuits. Because these heterogeneous network motifs are all identified as components within a single biochemical network, their interactions must drive the global dynamics of the network. Here, we formulate a theory for the network-level dynamics that result from coupling oscillatory and switch-like components have not been studied comprehensively previously.