  The latest results from the H1 and ZEUS collaborations are presented on leptoquark production and rare Standard Model processes. The data were taken in the period 1994-2005, at a centre of mass energy of up to 319 GeV. Intriguing events containing isolated leptons and missing transverse momentum, as well as multi-lepton events, are observed by H1 in regions of phase space where the SM prediction is low. Interpretations of the observed excesses in terms of physics Beyond the Standard Model are also discussed. 
Searches for New Physics in ep Scattering at HERA