The result of a search for high mass photon pairs from the processes with the ALEPH detector is reported. The result for f = e, μ and τ is to be compared with the observation of 4 events by the L3 Collaboration with invariant masses, Mγγ, of the two photons near 60 GeV. From a data sample approximately twice as large taken from 1990 to 1992, 6 events are found with Mγγ distributed between 50 GeV and 72 GeV, while 4.9 events are expected from a QED calculation. There is no evidence for a mass peak; only one event (μ+μ−γγ) at Mγγ = 59.4 ± 0.2 GeV is compatible with the L3 observation. In addition, for Mγγ > 50 GeV, no event is found for and only one event is found consistent with ; this event has Mγγ = 58.5 ± 1.9 GeV. High mass photon pair events have also been searched for in γγ collisions. This allows one to set an upper limit of 50 MeV for the width of an assumed resonance decaying to photon pairs.