The problem of testing the fit of the inverse Gaussian and the gamma distribution when the sample is censored and some of the parameters are unknown, is studied. Empirical Distribution Function (EDF) statistics, namely Cramér-von Mises' W 2 and the Anderson-Darling's A 2, are used. The limiting covariance functions of the corresponding empirical processes are derived. Asymptotic percentage points are given for some parameter values and censoring proportions. Moreover, a numerical routine is made available upon request, to obtain p-values for both test statistics, thus eliminating the need of tables and interpolation. Finally, a simple Monte Carlo study is presented to evaluate first, the approximation when using the asymptotic distributions in finite samples and second, to support the use of estimated parameter values instead of the unknown parameters needed in the limiting covariance function.