This paper considers the twin problems of testing for ARCH and GARCH disturbances in the linear regression model. A feature of these testing problems, ignored by the standard Lagrange multiplier test, is that they are one-sided in nature. A test which exploits this one-sided aspect is constructed based on the sum of the scores. Its small-sample size and power properties under both normal and leptokurtic disturbances are investigated via a Monte Carlo experiment. The results indicate that the new test typically has superior power to two versions of the Lagrange multiplier test and possibly also more accurate asymptotic critical values.