The energy spectrum of alpha particles trapped in the magnetosphere has been measured for the first time between 18 and 70 MeV for L values from 1.85 to 2.85 at 740-km altitude. In this energy range the spectrum is described by a power law with exponent 5.5¿1.3. The L distributions of alphas and protons with the same energy per nucleon are similar, but at the same energy per particle, distribution are distinctly different. The alpha to proton ratio maximum is 3.5¿103, an order of magnitude lower than that in the solar wind, and it falls steeply with energy.