Summary: When the hypothesis of linearity of a univariate time series model is tested using a battery of tests for neglected nonlinearity, the probability of one or more tests’ leading to a false rejection increases with the number of tests being performed. This paper discusses how this undesirable effect of multiple testing may be controlled by means of some simple and easily implemented procedures. Monte Carlo experiments are used to demonstrate the finite-sample effectiveness of the various methods, and an analysis of the nonlinearity properties of GDP data from five OECD countries is presented as an illustration.