This article develops a method for testing the goodness-of-fit of a given parametric autoregressive conditional duration model against unspecified nonparametric alternatives.The test statistics are functions of the residuals corresponding to the quasi maximum likelihood estimate of the given parametric model, and are easy to compute. The limiting distributions of the test statistics are not free from nuisance parameters. Hence, critical values cannot be tabulated for general use. A bootstrap procedure is proposed to implement the tests, and its asymptotic validity is established. The finite sample performances of the proposed tests and several other competing ones in the literature, were compared using a simulation study. The tests proposed in this article performed well consistently throughout,and they were either the best or close to the best. None of the tests performed uniformly the best. The tests are illustrated using an empirical example.