Abstract <p>This paper addresses the construction of the Anderson–Darling goodness-of-fit (GoF) test for inhomogeneous Poisson processes. We begin by considering simple basic hypotheses with a non-parametric alternative. It is demonstrated that the test based on this statistic is asymptotically distribution-free (ADF). Subsequently, we assume that the mean intensity function of the process under the null hypothesis follows a parametric form with an unknown shift parameter. The unknown parameter is estimated using the maximum likelihood estimator, and it is shown that in this case, the limiting distribution of the test statistic does not depend on the true value of this parameter.</p>