The paper considers different versions of the Lagrange multiplier (LM) tests for autocorrelation and/or for conditional heteroskedasticity. These versions differ in terms of the residuals, and of the functions of the residuals, used to build the tests. In particular, we compare ordinary least squares versus least absolute deviation (LAD) residuals, and we compare squared residuals versus their absolute value. We show that the LM tests based on LAD residuals are asymptotically distributed as a χ2 and that these tests are robust to nonnormality. The Monte Carlo study provides evidence in favor of the LAD residuals, and of the absolute value of the LAD residuals, to build the LM tests here discussed.