It has been reported recently by McDonald et al. (1976) that 1-MeV protons may undergo considerable acceleration in corotating streams. It has been suggested recently by Fisk et al. (1974b) that interstellar neutral particles which are ionized in the solar cavity may be accelerated in the solr wind and may account for the anomalous component that is observed in low-energy cosmic rays (at ~10 MeV/nucleon). It is shown here that the particle in both of these cases could be accelerated by transit time damping propagating fluctuations in the magnitude of the interplanetary magnetic field (e.g., magnetosonic waves). The protons in corotating streams may be accelerated by transit time damping the small-scale variations in the field magnitude that are observed at a low level in the inner solar system. The interstellar ions may be accelerated by transit time damping large-scale field variations in the outer solar system.