The atomic dynamical properties in the system with competing k-photon and l-photon transitions are studied fully by means of quantum theory. We discuss the influences of the mode-mode competition, the relative competing strengths of the atom and the two-mode field, and the initial state of the system on the atomic dynamics. We show that the presence of the mode-mode competition can result in quite a periodical collapses-revivals of the atomic inversion and the increase of the initial photons of the system can lead to the collapse-revival phenomenon and prolong the revival time of the atomic inversion.