  New spectroscopic observations of 36 HII regions in NGC 4258 obtained with
the Gemini telescope are combined with existing data from the literature to
measure the radial oxygen abundance gradient in this galaxy. The [OIII]4363
auroral line was detected in four of the outermost targets (17 to 22 kpc from
the galaxy center), allowing a determination of the electron temperature Te of
the ionized gas. From the use of different calibrations of the R23 abundance
indicator an oxygen abundance gradient of approximately -0.012 +/- 0.002
dex/kpc is derived. Such a shallow gradient, combined with the difference in
the distance moduli measured from the Cepheid Period-Luminosity relation by
Macri et al. between two distinct fields in NGC 4258, would yield an
unrealistically strong effect of metallicity on the Cepheid distances. This
strengthens the suggestion that systematic biases might affect the Cepheid
distance of the outer field. Evidence for a similar effect in the differential
study of M33 by Scowcroft et al. is presented. A revision of the transformation
between strong-line and Te-based abundances in Cepheid-host galaxies is
discussed. In the Te abundance scale, the oxygen abundance of the inner field
of NGC 4258 is found to be comparable with the LMC value.
