(71pp.) An approximation to the likelihood for the generalized linear models with random coefficients is derived and is the basis for an approximate Fisher scoring algorithm. The method is illustrated on the logistic regression model for one-way classification, but it has an extension to the class of generalized linear models and to more complex data structures, such as nested two-way classification. Both full and restricted maximum likelihood versions of this algorithm are defined. The estimators of the regression parameters coincide with the generalized estimating equations of Zeger and Liang (1986), but an essentially different class of estimators for the covariance structure parameters is obtained. A simulation study explores the properties of the proposed estimators.