The dynamics of individual behavior are related to the dynamics of the social structures in which individuals are embedded. This implies that in order to study social mechanisms such as social selection or peer influence, we need to model the evolution of social networks and the attributes of network actors as interdependent processes. The stochastic actor-oriented model is a statistical approach to study network-attribute coevolution based on longitudinal data. In its standard specification, the coevolving actor attributes are assumed to be measured on an ordinal categorical scale. Continuous variables first need to be discretized to fit into such a modeling framework. This article presents an extension of the stochastic actor-oriented model that does away with this restriction by using a stochastic differential equation to model the evolution of a continuous attribute. We propose a measure for explained variance and give an interpretation of parameter sizes. The proposed method is illustrated by a study of the relationship between friendship, alcohol consumption, and self-esteem among adolescents.