This paper proposes three classes of consistent tests for serial correlation of the residuals from a linear dynamic regression model. The tests are obtained by comparing a kernel-based spectral density estimator and the null spectral density using three divergence measures. The null normal distributions are invariant whether the regressors include lagged dependent variables. Both asymptotic local and global power properties are investigated. G. Box and D. Pierce's (1970) test can be viewed as a test based on the truncated kernel; many other kernels deliver better power than Box and Pierce's test. A simulation study shows that the new tests have good power against weak and strong dependence.