Using the effective Lagrangian approach, we obtain bounds on the lepto
n-number-nonconserving decays upsilon(mu) --> upsilon(e) gamma, upsilo
n(tau) --> upsilon(mu)gamma, upsilon(e) gamma from the known experimen
tal constraints on mu --> e gamma and tau --> mu gamma, e gamma. We ge
t a bound on the transition magnetic moment of the muon neutrino kappa
(mu e) less than or equal to 1 X 10(-11) for m(upsilon mu) less than o
r equal to 270 keV, which improves the bound obtained from astrophysic
al considerations. Our results also lead to bounds on the transition m
agnetic moments of the tau neutrino.