The spectra of solar proton and alpha particle fluxes from the solar particle event of November 18, 1968, deviate considerably from a power law form for as long as 2 days after the onset of the event. The spectral distortions are observed to progressively diminish with time. The departures in the spectral shape are not entirely attributable to diffusive velocity dispersion of the solar particles. Several lines of possible interpretation, taking into consideration effects of particle storage in the corona and the acceleration and deceleration of particles in the interplanetary medium, are discussed. It is suggested that acceleration of solar protons and alpha particles in the interplanetary medium is perhaps occurring. The time scales for the acceleration of protons in the energy range 0.6-2.0 MeV are derived.