For the analysis of data from developmental toxicity experiments that exhibits overdispersion, the beta-binomial model (Williams 1975) or the Dirichlet-multinomial model, an extension of the beta-binomial model, (Chen et al. 1991), is often used. However, investigations of these models suggest that when heterogeneous intra-litter correlations are incorrectly modeled as homogeneous the mean parameter estimates become biased (Kupper et al. 1986). Further even if the intra-litter correlation is correctly modeled, problems of bias of the parameter estimate and coverage probability of the parameter (e.g. coverage probability of 95 % confidence band) still exist (Liang and Hanfelt 1994). Liang and Hanfelt (1994) recommended the use of quasi-likelihood method for the inference instead of the beta-binomial maximum likelihood method. In this paper, two methods of analysis of extra-trinomial data using estimating equations are proposed. One is the quasi-likelihood/pseudolikelihood estimating equation method proposed by Carroll and Ruppert (1982) and Breslow (1989), which is also seen as a generalized estimating equations method, and the other is the quasi-likelihood/method of moments proposed by Williams (1982). From the results of White (1982), the parameter estimates are consistent when the mean model is correctly specified and the robust variance estimates of the parameter estimates can be calculated. An example of analysis using data from teratologica experiments is given.