Analysis of ordered binary and unordered binary data has received considerable attention in social and psychological research. This article introduces a Bayesian approach, which has several nice features in practical applications, for analyzing nonlinear structural equation models with dichotomous data. We demonstrate how to use the software WinBUGS and R2WinBUGS to obtain Bayesian estimates of the unknown parameters, estimates of latent variables, and the Deviance Information Criterion for model comparison. An illustrative example with an artificial data set is provided. Finally, simulation studies are conducted, not only to reveal the empirical performance of the Bayesian approach, but also to show that incorrectly treating binary data as ordinal, and vice versa, would produce misleading results. (Contains 3 figures and 8 tables.)