Dynamic Bayesian networks (DBN) are a class of graphical models that has become a standard tool for modeling various stochastic time-varying phenomena. In many applications, the primary goal is to infer the network structure from measurement data. Several efficient learning methods have been introduced for the inference of DBNs from time series measurements. Sometimes, however, it is either impossible or impractical to collect time series data, in which case, a common practice is to model the non-time series observations using static Bayesian networks (BN). Such an approach is obviously sub-optimal if the goal is to gain insight into the underlying dynamical model. Here, we introduce Bayesian methods for the inference of DBNs from steady state measurements. We also consider learning the structure of DBNs from a combination of time series and steady state measurements. We introduce two different methods: one that is based on an approximation and another one that provides exact computation. Simulation results demonstrate that dynamic network structures can be learned to an extent from steady state measurements alone and that inference from a combination of steady state and time series data has the potential to improve learning performance relative to the inference from time series data alone.