This paper presents general formulae for the likelihood ratio (LR), Wald (W), Lagrange multiplier (LM) and asymptotic locally most mean powerful (ALMMP) tests of linear regression disturbances using marginal likelihood methods. These tests can be derived by treating the maximal invariant statistic for these testing problems as the observed data. By way of illustration, the marginal-likelihood-based LR, W, LM and ALMMP tests are constructed for the separate problems of testing for general AR(4) disturbances and testing for the presence of Hildreth-Houck random coefficients. Empirical size calculations reported here and elsewhere suggest that this approach results in tests whose true sizes are much closer to the nominal size than their conventional counterparts.