Search for neutrinoless<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>τ</mml:mi></mml:math>decays:<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>τ</mml:mi><mml:mo>→</mml:mo><mml:mi>e</mml:mi><mml:mi>γ</mml:mi></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>τ</mml:mi><mml:mo>→</mml:mo><mml:mi>μ</mml:mi><mml:mi>γ</mml:mi></mml:math>

A search for the lepton-family-number-violating decays $\ensuremath{\tau}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ and $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\gamma}$ has been performed using CLEO II data. No evidence of a signal has been found and the corresponding upper limits are $B(\ensuremath{\tau}\ensuremath{\rightarrow}e\ensuremath{\gamma})&lt;2.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ and $B(\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\gamma})&lt;3.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ at 90% C.L.