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We study the decay rates of the $\mu \to e \gamma$ and $\tau \to \ell \gamma$transitions in the framework of the type III seesaw model, where fermionictriplets are exchanged to generate neutrino masses. We show that theobservation of one of those decays in planned experiments would contradictbounds arising from present experimental limits on the $\mu \to eee$ and $\tau\to 3 l$ decay rates, and therefore imply that there exist other sources oflepton flavour violation than those associated to triplet of fermions.

$\ell_1 \to \ell_2 \gamma$ in type III seesaw