Abstract: At the ep collider HERA, events with high-Pt leptons and missing calorimeter energy 
are an ideal environment to search for signs of physics beyond the Standard Model. In this paper we will focus on the results by the H1 and ZEUS Collaborations on searches for lepton flavor violation (LFV) in both the μ and τ channels and single top production by flavor changing neutral currents (FCNC). Both processes produce striking final states which can be detected with high efficiency and negligible background, allowing the HERA experiments to set constraints on the relevant couplings which, in many cases, supersede previous results.