Models of complex networks often incorporate node-intrinsic properties abstracted as hidden variables. The probability of connections in the network is then a function of these variables. Real-world networks evolve over time, and many exhibit dynamics of node characteristics as well as of linking structure. Here we introduce and study natural temporal extensions of static hidden-variable network models with stochastic dynamics of hidden variables and links. The rates of the hidden variable dynamics and link dynamics are controlled by two parameters, and snapshots of networks in the dynamic models may or may not be equivalent to a static model, depending on the location in the parameter phase diagram. We quantify deviations from static-like behavior, and examine the level of structural persistence in the considered models. We explore tempor
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