We present measurements of the gas-phase C/O abundance ratio in six \ion H2 regions in the spiral galaxies M101 and NGC 2403 , based on ultraviolet spectroscopy using the Faint Object Spectrograph on the Hubble Space Telescope . The C/O ratios increase systematically with O/H in both galaxies , from log C/O \approx - 0.8 at log O/H = - 4.0 to log C/O \approx - 0.1 at log O/H = - 3.4 . C/N shows no correlation with O/H . The rate of increase of C/O is somewhat uncertain because of uncertainty as to the appropriate UV reddening law , and uncertainty in the metallicity dependence on grain depletions . However , the trend of increasing C/O with O/H is clear , confirming and extending the trend in C/O indicated previously from observations of irregular galaxies . Our data indicate that the radial gradients in C/H across spiral galaxies are steeper than the gradients in O/H . Comparing the data to chemical evolution models for spiral galaxies shows that models in which the massive star yields do not vary with metallicity predict radial C/O gradients that are much flatter than the observed gradients . The most likely hypothesis at present is that stellar winds in massive stars have an important effect on the yields and thus on the evolution of carbon and oxygen abundances . C/O and N/O abundance ratios in the outer disks of spirals determined to date are very similar to those in dwarf irregular galaxies . This implies that the outer disks of spirals have average stellar population ages much younger than the inner disks .