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[en] In this article, we discuss the one-excitation dynamics of a quantum system consisting of two two-level atoms each interacting with one of two coupled single-mode cavities via spontaneous emission. When the atoms and cavities are tuned into resonance, a wide variety of time-evolution behaviors can be realized by modulating the atom-cavity coupling strength g and the cavity-cavity hopping strength λ. The dynamics is solved rigorously via the eigenproblem of an ordinary coupled linear system and simple analytical solutions are derived at several extreme situations of g and λ. In the large hopping limit where g<<λ, the behavior of the system is the linear superposition of a fast and slow periodic oscillation. The quantum state transfers from one atom to the other atom accompanied with weak excitation of the cavity mode. In the large coupling limit where g>>λ, the time-evolution behavior of the system is characterized by the usual slowly varying carrier envelope superimposed upon a fast and violent oscillation. At a certain instant, the energy is fully transferred from the one quantum subsystem to the other. When the two interaction strengths are comparable in magnitude, the dynamics acts as a continuous pulse having irregular frequency and line shape of peaks and valleys, and the complicated time-evolution behaviors are ascribed to the violent competition between all the one-excitation quantum states. The coupled quantum system of atoms and cavities makes a good model to study cavity quantum electrodynamics with great freedoms of many-body interaction.