This paper examines the usefulness of H. White's (1982) information matrix test and test for heteroskedasticity of unspecified form as general checks of adequacy in the context of linear models. Asymptotic analysis and Monte Carlo results are provided, with the latter covering a number of general misspecification tests. Comments are made on the value of testing for normality. Copyright 1994 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.