Z.Phys.C74:191-206,1997 Measurements of ep scattering with squared 4-momentum transfer Q^2 up to 35000 GeV^2 are compared with the expectation of the standard deep-inelastic model of lepton-nucleon scattering (DIS). For Q^2 > 15000 GeV^2, N_{obs} =12 neutral current candidate events are observed where the expectation is N_DIS = 4.71 \pm 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 \pm 0.87 events. The probability P(N \geq N_{obs}) that the DIS model signal N fluctuates to N \geq N_{obs} in a random set of experiments is 6 10^{-3} for neutral current and 0.14 for charged current. The difference in the observed and expected number of Neutral Current events is mostly due to events at large masses M = sqrt{xs} in which the positron is backscattered at large y = Q^2/M^2.