This paper deals with the problem of parameter estimation in generalized linear mixed models. Gilmour, Anderson and Rae [1] proposed a method of estimation in a probit link model for binomial data. This method follows a marginal approach maximizing the quasi-score function. Foulley and Im [2] adapted it to Poisson data in a log link model. We propose a unifying formal description for these two cases, including also the case of exponential data in a log link model. This approach enables us to consider other cases such as logit link model for binomial data. Numerical examples are given to illustrate the method.