We present deep spectrophotometry of 18 H II regions in the nearby massive spiral galaxies M 101 and M 31. We have obtained direct determinations of electron temperature in all the nebulae. We detect the C II 4267 Å line in several H II regions, permitting to derive the radial gradient of C/H in both galaxies. We also determine the radial gradients of O/H, N/O, Ne/O, S/O, Cl/O, and Ar/O ratios. As in other spiral galaxies, the C/H gradients are steeper than those of O/H producing negative slopes of the C/O gradient. The scatter of the abundances of O with respect to the gradient fittings do not support the presence of significant chemical inhomogeneities across the discs of the galaxies, especially in the case of M101. We find trends in the S/O, Cl/O, and Ar/O ratios as a function of O/H in M101 that can be reduced using Te indicators different from the standard ones for calculating some ionic abundances. The distribution of the N/O ratio with respect to O/H is rather flat in M31, similarly to previous findings for the Milky Way. Using the disc effective radius - Re - as a normalization parameter for comparing gradients, we find that the latest estimates of Re for the Milky Way provide an excess of metallicity in apparent contradiction with the mass-metallicity relation; a value about two times larger might solve the problem. Finally, using different abundance ratios diagrams we find that the enrichment time-scales of C and N result to be fairly similar despite their different nucleosynthetic origin.