Seasonal autoregressive models with an intercept or linear trend are discussed. The main focus of this paper is on the models in which the intercept or trend parameters do not depend on the season. One of the most important results from this study is the asymptotic distribution for the ordinary least squares estimator of the autoregressive parameter obtained under nearly integrated condition, and another is the approximation to the limiting distribution of the t-statistic under the null for testing the unit root hypothesis.