Many goodness-of-fit tests have been developed to assess the different assumptions of a (possibly heteroscedastic) regression model. Most of them are “directional” in that they detect departures from a given assumption of the model. Other tests are “global” (or “omnibus”) in that they assess whether a model fits a dataset on all its assumptions. We focus on the task of choosing the structural part of the regression function because it contains easily interpretable information about the studied relationship. We consider 2 nonparametric “directional” tests and one nonparametric “global” test, all based on generalizations of the Cramér-von Mises statistic. To perform these goodness-of-fit tests, we develop the R package cvmgof providing an easy-to-use tool for practitioners, available from the Comprehensive R Archive Network (CRAN). The use of the library is illustrated through a tutorial on real data. A simulation study is carried out in order to show how the package can be exploited to compare the 3 implemented tests.