Seasonal autoregressive models with a polynomial trend of higher degee are treated. In the unit root case, the limiting distribution of the normalized least squares estimator for the autoregressive parameter and that of the corresponding t-statistic are discussed as the length of the sample period tends to infinity. In the case where the polynomial trend has the second or third degree, the joint moment generating functions associated with these limiting distributions are derived, and some simulation results are reported. The asymptotic behavior of these limiting distributions is discussed when the polynomial degree or the number of seasons tends to infinity.