Abstract: In the generalized linear model, some relations between the estimating equations are proved by use of the Markov inequality theorem, and thus it is further proved that βn and βnare of asymptotic consistency.Finally, the asymptotic normality of the estimator of the generalized Poisson distribution is proved by using the Lyapunov condition when the general law is satisfied.These results are proved under the weaker conditions, and the corresponding results are improved.