  We present results for the $p p \to p p \omega$ reaction studied by
considering two different scenarios: with and without the inclusion of nucleon
resonance excitations. The recently measured angular distribution by the
COSY-TOF Collaboration at an excess energy of $Q = 173$ MeV and the energy
dependence of the total cross section data for $\pi^- p \to \omega n$ are used
to calibrate the model parameters. The inclusion of nucleon resonances improves
the theoretical prediction for the energy dependence of the total cross section
in $pp \to pp\omega$ at excess energies $Q < 31$ MeV. However, it still
underestimates the data by about a factor of two, and remains a problem in
understanding the reaction mechanism.
