Search for neutrinoless $\tau$ decays: $\tau \to e\gamma$ and $\tau \to \mu \gamma$

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