Imaging spectrophotometry in the nebular lines Hα, Hβ, [N II], and [O III], using narrow-band interference filters and a CCD camera, has been performed of nearly 300 H II regions in the galaxies NGC 628 and NGC 6946. The reliability of the method for doing spectrophotometry of H II regions is demonstrated, and several physical parameters related to the chemistry of the galaxies are derived. Reddening, Hβ emission equivalent widths, diagnostic line ratios [O III]/Hβ and [N II]/[O III], and O/H abundances were measured for 130 H II regions as far as 2.0R_eff_ in NGC 628, and for 160 H II regions as far as 1.4R_eff_ in NGC 6946. Neither reddening nor the Hβ equivalent widths display any trend as a function of radial distances from the galactic centers. On the other hand, [O III]/Hβ and [N II]/[O III] are strongly correlated with galactocentric distances; the values of [N II]/[O III] display less dispersion at any given radius. Using the empirical calibration of Edmunds & Pagel, O/H abundances were calculated for all H II regions. In NGC 628, the global oxygen abundance gradient is described by {DELTA}log(O/H)/{DELTA}R = -0.081+/-0.002 dex kpc^-1^,at an assumed distance of 7.2 Mpc; in NGC 6946(5.9 Mpc), the global O/H gradient is given by {DELTA}log (O/H)/{DELTA}R = -0.089 +/- 0.003 dex kpc^-1^. Extrapolated central abundances are 12 + log (O/H) = 9.20 +/- 0.01 in NGC 628, and 9.36 +/- 0.02 in NGC 6946. The slope of the gradient is constant across the complete range of radial distances sampled in NGC 628. In the inner parts of NGC 6946 (R <= 0.5R_eff_), the derived abundances display a large dispersion, and the radial trend is consistent with an almost flat gradient; for R >= 0.5R_eff_ the O/H gradient is well defined and its slope is slightly steeper than in NGC 628. The O/H abundances in the central regions of NGC 6946 may be affected by the presence of a molecular and ionized gas bar. Using an enlarged sample of six galaxies, where about 50 H II regions or more were observed, various trends are investigated. The galaxies included in the sample correspond to a relatively wide range of luminosities; they are NGC 628, NGC 2997, NGC 6946, M33, M 101, and the Milky Way Galaxy. The amplitudes of their global gradients are identical within the uncertainty of about +/- 0.01 dex kpc^-1^ on gradients of individual galaxies. Claims of correlation between the amplitudes of gradients and other global properties of galaxies are considered at present premature until a greater number of large samples of H II regions becomes available. The efficiency of the method of imaging spectrophotometry is emphasized for survey programs where limited spectral data must be obtained for a large number of objects, such as obtaining data samples for the derivation of reliable abundance gradients in galaxies.