Observations in the solar wind with the LASL/MPI fast plasma experiment on ISEE 1 and 2 reveal the common presence of ions with energies extending from ~100 eV up to at least 40 keV in a broad region, typically ~107 km wide, following interplanetary shocks. Peak differential fluxes up to ~5¿103 (cm2 s sr keV)-1 at 28 keV are observed either at the shock or within the first ~1.5 hours following shock passage. In the solar wind frame the distribution function f(&ngr;) of these ions is roughly isotropic, peaks near zero velocity, and above ~5 keV can adequately be characterized as power law in energy with a spectral index of ~2.7. The effective 'temperature' of these ions generally exceeds 108 ¿K. These suprathermal interplanetary ions are almost certainly solar wind ions which have been accelerated by some mechanism associated with the shock wave disturbance. Present evidence leads the authors to favor stochastic particle acceleration involving electrostatic and/or electromagnetic turbulence in the postshock flow.