Search for the rare decay. mu. /sup +/. -->. e/sup +/. gamma gamma

A new experimental search with the Crystal Box detector shows no evidence for the lepton-family-number--nonconserving decay ..mu../sup +/..-->..e/sup +/..gamma gamma... This corresponds to an upper limit for the branching ratio of GAMMA(..mu -->..e..gamma gamma..)/GAMMA(..mu -->..e..nu..nu-bar)<7.2 x 10/sup -1/ (90% confidence level), an improvement of more than 2 orders of magnitude in sensitivity.