This paper develops an exact maximum likelihood technique for estimating regression equations with general p'th-order autoregressive disturbances. The approach appears to be computationally practical and straightforward, insures the estimated error coefficients satisfy a priori stationarity conditions, and insures convergence of the estimation procedure. Recent expression of the analytic inverse of the covariance matrix of a stationary AR(p) process provides the basis for the iterative algorithms, which employ a modified Gauss-Newton technique utilizing exact first and approximate second derivatives. The relationship between stationarity and the form of the objective function is examined. Empirical estimates are then presented for regression models with and without a lagged dependent variable.