A study on the TESLA measurement expectations for Lepton Flavour Violation (LFV) leptonic Z → l_il_j decays 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 and Z processes that are fully exploited. The consequence is that several restrictions can be put on the Z → μe decay whilst Z → τl could be still at reach of the Giga-Z mode in TESLA.
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