  Motived by recent ISM studies, we present high quality MMT and Gemini
spectroscopic observations of H II regions in the nearby spiral galaxies NGC
628 and NGC 2403 in order to measure their chemical abundance gradients. Using
long-slit and multi-object mask optical spectroscopy, we obtained measurements
of the temperature sensitive auroral lines [O III] {\lambda}4363 and/or [N II]
{\lambda}5755 at a strength of 4{\sigma} or greater in 11 H II regions in NGC
628 and 7 regions in NGC 2403. These observations allow us, for the first time,
to derive an oxygen abundance gradient in NGC 628 based solely on "direct"
oxygen abundances of H II regions: 12 + log(O/H) = (8.43+/-0.03) +
(-0.017+/-0.002) x Rg (dex/kpc), with a dispersion in log(O/H) of {\sigma} =
0.10 dex, from 14 regions with a radial coverage of ~2-19 kpc. This is a
significantly shallower slope than found by previous "strong-line" abundance
studies. In NGC 2403, we derive an oxygen abundance gradient of 12 + log(O/H) =
(8.48+/-0.04) + (-0.032+/-0.007) x Rg (dex/kpc), with a dispersion in log(O/H)
of {\sigma} = 0.07 dex, from 7 H II with a radial coverage of ~1-10 kpc.
  Additionally, we measure the N, S, Ne, and Ar abundances. We find the N/O
ratio decreases with increasing radius for the inner disk, but reaches a
plateau past R25 in NGC 628. NGC 2403 also has a negative N/O gradient with
radius, but we do not sample the outer disk of the galaxy past R25 and so do
not see evidence for a plateau. This bi-modal pattern measured for NGC 628
indicates dominant contributions from secondary nitrogen inside of the R25
transition and dominantly primary nitrogen farther out. As expected for
{\alpha}-process elements, S/O, Ne/O, and Ar/O are consistent with constant
values over a range in oxygen abundance.
