Search and identification of Scalar and Vector Leptoquarks at HERA with polarization

We analyze the effects of Scalar and Vector Leptoquarks on various observables in electron (positron) - proton deep inelastic scattering. In view of the future program of the HERA collider, with a high luminosity and also with polarization, we present the constraints that can be reached using this facility for several Leptoquark scenarios. We address the question of the identification of the nature of a discovered Leptoquark. We emphasize the relevance of having polarized lepton and proton beams in order to disentangle completely the various Leptoquark models. This study is also relevant in the context of the TESLA$\times$HERA project.