The generalized linear models were defined by Nelder and Wedderburn (1972) and these models allow us to fit regression models for univariate response data which follow a very common exponential family of distribution. The unknown regression coefficients of the generalized linear models are estimated by the maximum likelihood estimator. However, in the existence of multicollinearity, the variance of the maximum likelihood estimator becomes inflated and the statistical inferences based on the maximum likelihood method may not be reliable. In this study, we develop a first order two parameter estimator which combines the advantages of ridge and contraction estimators in the generalized linear models by extending the work of Özkale and Kaçıranlar (2007) in the linear model. The superiority of the first order two parameter estimator to the maximum likelihood, ridge and Liu estimators is investigated with regard to the mean square error criterion. We also examine some optimal estimators of biasing parameters. In addition to the theoretical comparisons, the performance of the estimators is judged by numerical evaluations where the mean square error is considered as a performance criterion.