Two-mode networks are networks having two distinct node sets (“modes”) in which ties are possible only between nodes from different sets. Various examples are given of data structures that can be regarded as two-mode networks. For example, two-mode networks can be used to represent additional aspects of social embeddedness. A version of the stochastic actor-oriented model is presented in which the agency is in nodes of the first mode, that is, these nodes are the actors who make choices of tie changes. Some effects are presented that are useful especially for two-mode networks. Particular attention is given to the co-evolution of a one-mode network and a two-mode network. Here the issue of selection versus influence comes up again. To give an example in the co-evolution of a one-mode friendship network and a two-mode network of club membership: Do members of the same club become friends (selection), or do friends become members of the same club (influence)? Mixed triadic effects are presented that may be used for treating such questions.