For several years it has been known that traveling interplanetary shocks can accelerate ions to energies of ≥70 MeV/nucleon. Recently, a subset of these shocks has been found to accelerate electrons as well, sometimes to energies of 7 MeV. Between 1978 and 1985 the Pioneer 10/11 spacecraft have observed 11 traveling interplanetary shocks in the outer heliosphere, 7 to 28 AU, which accelerate protons and helium to energies ≥11--20 MeV/nucleon. Six of these shock events also accelerate electrons to the energy range 2--7 MeV. These are the only traveling interplanetary shocks seen by the Pioneer spacecraft where electrons are accelerated to relativistic energies. In this paper we give the results of analyses of the solar wind plasmas, interplanetary magnetic field, and energetic particle data for the 11 shocks. Our analysis has determined that there appear to be three necessary conditions in order for a traveling interplanetary shock to simultaneously accelerate ions to at least 11--20 MeV/nucleon and electrons to relativistic energies: (1) that the upstream magnetic field have a precursor wave in the frequency range 0.003--0.04 s-1; (2) that the shock has a compression ratio r (=&rgr;2/&rgr;1) of between 3 and 4, and has the scattering centers converge at ‖ΔV‖≥ 50 km/s; and (3) that the relativistic electrons be accelerated via the Fermi mechanism. We propose a model to explain the simultaneous appearance of relativistic electrons and high-energy ions at an outer heliospheric traveling shock. In this model the Fermi mechanism accelerates the electrons in two stages to relativistic energies, and the shock-drift mechanism accelerates the ions to energies ≥11--20 MeV/nucleon. An analysis of the momentum spectra of various charged particle species leaves indeterminate the origin of the seed populations of both shocks which accelerate only ions and those which accelerate both ions and relativistic electrons. ¿ American Geophysical Union 1989