VRI CCD photometry of supergiant stars in the barred galaxies NGC 925 and NGC 1637

V, R, and I CCD images obtained with the Canada-France-Hawaii Telescope are used to investigate the bright stellar content of the barred spiral galaxies NGC 925 and NGC 1637. Not counting objects located in H II regions, we detect 295 supergiants in NGC 925 and 266 in NGC 1637. Comparisons with theoretical isochrones indicate that massive star formation in NGC 925 has been ongoing for at least a few tens of millions of years. Most of the supergiants in NGC 925 are younger than 20 Myr and have masses between 10 and 60 M.. The majority of supergiants in NGC 1637 appear to be younger than 40 Myr and have initial masses between 8 and 60 M.. The luminosity functions of supergiants in both galaxies follow power laws with exponents d log n/d log V = 0.50 +/- 0.05 for NGC 925 and 0.62 +/- 0.04 for NGC 1637. These values are shallower than what is seen in most spiral galaxies, although there are some exceptions. Archival Hubble Space Telescope images of NGC 925 are used to assess the effects of blending on our photometric measurements. We conclude that crowding could cause a fattening of the luminosity function and bias the brightnesses of the most luminous stars. The brightest red supergiants are used to estimate the distance moduli of these galaxies. After applying corrections for blending, we find that mu(0), 29.67 for NGC 925 and mu(0) = 29.47 for NGC 1637, corresponding to linear distances of 8.61(-1.0)(+1.1) and 7.8 Mpc, respectively. The distance computed for NGC 925 is in good agreement with that recently derived from Cepheids.