This article presents estimates of the power of four tests for the independence of the disturbances from linear regression models with two sets of alternative hypotheses—second-order autoregressive processes and first-order moving average processes. The results indicate that for a number of specifications of the second-order autoregressive error structure the Durbin-Watson and Durbin alternative exact tests are more powerful than a test designed for this class of alternatives. With models including first-order moving average errors the Durbin-Watson and Durbin alternative exact test are consistently more powerful than the other tests studied for all model specifications and sample sizes.