A study on the TESLA measurement expectations for Lepton Flavour Violation (LFV) leptonicZ→liljdecays is presented. We have explored both the decoupling and non‐decoupling scenarious in the Effective Lagrangian formalism as a way to include general beyond the Standard Model (SM) effects. As the effective lagrangian complies with the SM gauge symmetries by construction, we have relationships between photon andZprocesses that are fully exploited. The consequence is that several restrictions can be put on theZ→ &mgr;edecay whilstZ→ &tgr;lcould be still at reach of the Giga‐Z mode in TESLA. © 2003 American Institute of Physics