  The production of the heavy stable proton-rich isotopes between 74Se and
196Hg -- the p nuclides -- is due to the contribution from different
nucleosynthesis processes, activated in different types of stars. Whereas these
processes have been subject to various studies, their relative contributions to
Galactic Chemical Evolution are still a matter of debate. We investigate for
the first time the nucleosynthesis of p nuclides in GCE by including
metallicity and progenitor mass-dependent yields of core-collapse supernovae
(ccSNe) into a chemical evolution model. We used a grid of metallicities and
progenitor masses from two different sets of stellar yields and followed the
contribution of ccSNe to the Galactic abundances as function of time. In
combination with previous studies on p-nucleus production in thermonuclear
supernovae (SNIa), and using the same GCE description, this allows us to
compare the respective roles of SNeIa and ccSNe in the production of p-nuclei
in the Galaxy. The gamma process in ccSN is very efficient for a wide range of
progenitor masses (13M_sun_- 25M_sun) at solar metallicity. Since it is a
secondary process with its efficiency depending on the initial abundance of
heavy elements, its contribution is strongly reduced below solar metallicity.
This makes it challenging to explain the inventory of the p nuclides in the
Solar System by the contribution from ccSNe alone. In particular, we find that
ccSNe contribute less than 10% of the solar p nuclide abundances, with only a
few exceptions. Due to the uncertain contribution from other nucleosynthesis
sites in ccSNe, such as neutrino winds or $\alpha$-rich freeze out, we conclude
that the light p-nuclides 74$Se,78$Kr, 84Sr, and 92Mo may either still be
completely or only partially produced in ccSNe.
