This paper presents some new results on exogeneity in models with latent variables. The concept of exogeneity is extended to the class of models with latent variables, in which a subset of parameters and latent variables is of interest. Exogeneity is discussed from the Bayesian point of view. We propose sufficient weak and strong exogeneity conditions in the vector error correction model (VECM) with stochastic volatility (SV) disturbances. Finally, an empirical illustration based on the VECM-SV model for the daily growth rates of two main official Polish exchange rates: USD/PLN and EUR/PLN, as well as EUR/USD from the international Forex market is presented. The exogeneity of the EUR/USD rate is examined. The strong exogeneity hypothesis of the EUR/USD rate is not rejected by the data.