  The role of the low lying nucleon resonances beyond the $\Delta(1232)$ in the
reaction $pp\to pp\pi^0$ near threshold is shown to be numerically significant
by a calculation, which takes into account the pion re-scattering contribution
described by chiral perturbation theory and the short-range mechanisms that are
implied by the nucleon-nucleon interaction model. The intermediate N(1440)
(P$_{11}$) resonance is excited by the short-range exchange mechanisms, while
the N(1535) ($S_{11}$) and N(1520) ($D_{13}$) resonances are excited by $\eta$
and $\rho$ meson exchange, respectively. The $P_{11}$ increases the calculated
cross section, whereas the $S_{11}$ and $D_{13}$ resonances decrease it. The
calculation takes full account of the initial and final state interactions.
