Betelgeuse (Alpha Ori) and Antares (Alpha Sco) are red supergiants with an extensive convective outer envelope. The present investigation is concerned with an analysis of high-resolution 5 micron spectra of the two stars. The considered spectra had been acquired with the Fourier transform spectrometer at the coude focus of the Mayall 4 m reflector. A red supergiant's extensive atmosphere ensures that the less abundant species involving O-17 and O-18 contribute a significant number of lines. The obtained isotopic abundance ratios are presented in a table, taking into account C-12/C-13, O-16/O-17, O-16/O-18, and O-17/O-18. The nucleosynthesis of oxygen isotopes is discussed. An analysis of the oxygen isotopes in the atmosphere of the two stars shows that O-17 is enriched because of the CNO cycles and convective mixing.