Abstract: Generalized linear mixed models (GLMMs) are often used to analyze non-Gaussian data arising from different studies. In Bayesian GLMMs, the commonly used improper priors may yield undesirable improper posterior distributions. Here we consider the popular improper uniform prior to the regression coefficients and several proper or improper priors including the widely used gamma and power priors on the variance components of the random effects. We derive necessary and sufficient conditions for posterior propriety for Bayesian binomial and Poisson GLMMs. Also, we use examples involving one-way and two-way random-effects models to demonstrate the theoretical results.