Summary: G. Molenberghs and L. M. Ryan (1996) proposed a likelihood-based model for clustered binary data, based on a multivariate exponential family model [D. R. Cox, Appl. Statist. 21, 113-120 (1972)]. The model benefits from the elegance and simplicity of exponential family theory and is flexible in terms of allowing respone rates to depend on cluster size. A main problem however, particularly with large clusters is the evaluation of the normalizing constant. In the paper, pseudo-likelihood is explored as an alternative mode of inference. The pseudo-likelihood equations are derived, the model is applied to data from a developmental toxicity study, and an asymptotic and small sample relative efficiency study is performed.