Internal partition functions for 18 diatomic molecules were computed by three different methods. The computations were performed for temperatures from 500° to 30 000°K. The methods of computation are (a) Mayer and Mayer approximation, (b) direct summation to dissociation limit, and (c) direct summation including states above dissociation limit. The variation in numerical results using these three methods is negligible up to temperatures of 5000°K, although there are some exceptions for molecules containing hydrogen. At higher temperatures the Mayer and Mayer approximation gives, for most molecules, excessive values for the partition function. An indication of the importance of including excited electronic states and excluding some first rotational states is also given.