Based on 1) a conjecture about the mean free path for particle scattering in perpendicular shock geometries, and 2) a model for Wolf-Rayet star winds, we argue that explosions of Wolf-Rayet stars can lead through diffusive particle acceleration to particle energies up to 3 1O9 GeV. As a test we first demonstrate that the magnetic fields implied by this argument are compatible with the dynamo limit applied to the convective interior of the main sequence stars which are predecessors of Wolf-Rayet stars; second we show that this implies the same strength of the magnetic fields as is suggested by the magnetically driven wind theory. Third, we use data from radio supernovae to check the spectrum, luminosity and time dependence which suggest that the magnetic fields again have to be as high as suggested by the magnetically driven wind theory. This constitutes evidence for the magnetic field strengths required to accelerate particles to 3 1O9 GeV. Fourth, we demonstrate that within our picture the nonthermal radio emission from OB and Wolf-Rayet stars can reproduce the proper radio spectra, time variability and radio luminosities. Fifth, the comparison of Wolf-Rayet stars and radio supernovae suggests that electron injection into the acceleration process is a step function of efficiency with the shock speed as the independent parameter; the critical speed appears to be that speed at which the thermal downstream electrons become relativistic. We make detailed predictions on the temporal and spectral behaviour of the nonthermal radio emission of OB and Wolf-Rayet stars that will allow further checks our model.