High energy proton detectors on the Combined Release and Radiation Effects Satellite (CRRES) were used to measure near-Earth solar protons in an 18 degrees inclination orbit between 350 km and 36000 km from July 1990 to October 1991. CRRES data from the major solar particle event on 23-25 March 1991 show conclusively that MeV solar protons can penetrate deep inside the magnetosphere (to an L-shell of 2.5 RE) when a large shock-induced Sudden Storm Commencement (SSC) occurs and significant solar particle populations are present at geosynchronous altitudes. The penetration of solar particles well inside boundaries predicted by Stormer theory occurred during every large solar event of the CRRES mission, as well as many of the smaller ones. Often the deep penetrations occurred simultaneously with the formation of new trapped radiation populations which peak at L-values between 2.3 and 4 RE (depending on particle energy) and which last from days to months.