Abstract: In nonlinear regression model, the optimality of quasi likelihood estimatiom in theclass of normal generalized quasi likelihood estirnation is proved.The relation between the opti-mality of quasi score function and quasi likelihood estimation is discussed. To improve on quasilikelihood estimation,a constrained quasi likelihood estimation is presented. For this estimation,the superiority over quasi likelihood estimation is proved.

Key words: Nonlinear regression model, quasi score function, quasi likelihood estimation, class of normal generalized quasi likelihood estimation, constrained quasi likelihood estimation, mean squared error