Many active galactic nuclei and/or associated jets and hot spots show a sharp cutoff in their nonthermal emission near ∼3 1014 Hz. Using the first order Fermi theory for particle acceleration at shocks we demonstrate that synchrotron emission and shock acceleration combine to give a maximum cutoff near to the observed frequency. We explore consequences: First, CCD-observations of the M87 jet demonstrate that the cutoff frequency decreases along the jet. Second, the detailed shape of the cutoff spectrum depends on the precise model for the turbulent wave field. Thirdly, an X-ray Synchrotron contribution from p-p and p-γ interactions exists which can match observed AGN spectra. Finally we apply the model to interpret the origin of very high energy cosmic rays, to the spectral behaviour of quasars and BL Lac's and deduce neutrino emission spectra of active galactic nuclei.