General Search for New Phenomena in ep scattering at HERA --------------------------------------------------------- A model-independent search for deviations from the Standard Model prediction has been performed in e^+ p and e^- p collisions at HERA using H1 data corresponding to an integrated luminosity of 115 pb-1. All experimentally measurable event topologies involving electrons, photons, muons, neutrinos and jets with high transverse momenta have been investigated. Events are classified into exclusive event classes according to their final state. A new algorithm has been developed to look for regions with large deviations from the Standard Model in the invariant mass and sum of transverse momenta distributions and to quantify the significance of the fluctuations observed. A good agreement with the Standard Model prediction is found in most of the event classes.