  The dynamics of the resonant Auger (RA) process of the core-excited
C$^\ast$O(1s$^{-1}\pi^\ast,v_r=0$) molecule in an intense X-ray laser field is
studied theoretically. The theoretical approach includes the analogue of the
conical intersections of the complex potential energy surfaces of the ground
and `dressed' resonant states due to intense X-ray pulses, taking into account
the decay of the resonance and the direct photoionization of the ground state,
both populating the same final ionic states coherently, as well as the direct
photoionization of the resonance state itself. The light-induced non-adiabatic
effect of the analogue of the conical intersections of the resulting complex
potential energy surfaces gives rise to strong coupling between the electronic,
vibrational and rotational degrees of freedom of the diatomic CO molecule. The
interplay of the direct photoionization of the ground state and of the decay of
the resonance increases dramatically with the field intensity. The coherent
population of a final ionic state via both the direct photoionization and the
resonant Auger decay channels induces strong interference effects with distinct
patterns in the RA electron spectra. The individual impact of these physical
processes on the total electron yield and on the CO$^+(A^2\Pi)$ electron
spectrum are demonstrated.
