Measurements of the cosmic-ray hydrogen and helium spectra at energies from
20 to 800 TeV are presented. The experiments were performed on a series of
twelve balloon flights, including several long duration Australia to South
America and Antarctic circumpolar flights. No clear evidence is seen for a
spectral break. Both the hydrogen and the helium spectra are consistent wi
th power laws over the entire energy range, with integral spectral indices
1.80 +/- 0.04 and 1.68(-0.06)(+0.04) for the protons and helium, respective
ly. The results are fully consistent with expectations based on supernova s
hock acceleration coupled with a "leaky box" model of propagation through t
he Galaxy.