AR(1) models in time series with nonnormal errors represented by two families of distributions: (i) Gamma with support IR:(0,infinity), and (ii) Student's t with support IR:(-infinity,infinity) are considered. Since the maximum likelihood (ML) estimators are intractable, the modified maximum likelihood (MML) estimators of the parameters are derived and it is shown that they are remarkably efficient besides being easy to compute. It is also shown that the least squares (LS) estimators have very low efficiencies and as a consequence, we make a recommendation that their use be limited to normal errors. We give engineering applications. The methodology presented readily extends to AR(q) models.