Abstract: Reproductive dispersion linear models (RDLMS) are the natural generalization of statistical models such as linear regression models, generalized linear models and exponential linear models. Maximum L_q-likelihood estimation (ML_qE) is a generalization of maximum likelihood estimation. Building on Fahrmeir et al., we establish weak and strong consistency as well as asymptotic normality of the ML_qE of RDLMS, thereby extending the existing results. A simulation example shows that our estimation method is effective is effective the maximum Lq-likelihood estimation is robust.