In spite of the rather good agreement between the theory of stellar evolution and the observations, there exist some difficulties when one compares closely the sequences of open star clusters and the theoretical isochrones. Several, if not all, of the old open star clusters seem to be concerned, especially those which are accurately measured, namely Praesepe, NGC 2360, 752, 3680 and M67. The problem concerns the gap occuring in the HR diagram at the end of the phase of hydrogen burning in the core; it corresponds to the phase of hydrogen exhaustion (or of overall contraction). The sequence of M67 has been studied by Racine (1971) and Torres-Peimbert (1971). The well apparent gap is located farther from the zero-age main sequence than indicated by the models and the hook towards a larger Teff predicted during this phase is not observed. Differences in chemical composition may not be held responsible for these anomalies. From Torres-Peimbert's models, it may be assumed that neither solar type, nor super metal rich composition are able to reduce the discrepancies. As a further illustration, let us mention the case of NGC 752. In Table I, the main features related to the gap are examined: the disagreement, like in M67, essentially concern features 1 and 2. The observations are based on a recent study of Grenon and Mermillod (1973) and on Bell's data (1972). Bell has also mentioned the existence of discrepancies. As in M67, the gap is too far from the zero-age main sequence and does not present any sudden turning towards a larger Teff.