Observation of events at very high Q(2) in ep collisions at HERA

Measurements of ep scattering with squared 4-momentum transfer Q(2) up to 35000 GeV2 are compared with the expectation of the standard deep-inelastic model of lepton-nucleon scattering (DIS). For Q(2) > 15000 GeV2 N-obs = 12 neutral current candidate events are observed where the expectation is N-DIS = 4.71 +/- 0.76 events. In the same Q(2) range, N-obs = 4 charged current candidates are observed where the expectation is N-DIS = 1.77 +/- 0.87 events. The probability P(N greater than or equal to N-obs) that the DIS model signal N fluctuates to N greater than or equal to N-obs in a random set of experiments is 6 x 10(-3) for neutral current and 0.14, for charged cur rent, The difference in the observed and expected number of Neutral Current events is mostly due to events at large masses M = root xs in which the positron is backscattered at large y = Q(2)/M-2.