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The ability of engineering biological nanomachines to communicate with biological systems at the molecular level is anticipated to enable a larger application scenario. Single biological nanomachine has limited ability to accomplish target goals, so a nanonetwork, which is composed of interconnected biological nanomachines, is expected. To perform cooperative operations in nanonetworks, the synchronization of the biological nanomachines is essential. This paper describes the oscillation and synchronization derived from a biological nanonetwork, which consists of two biological nanomachines. Each biological nanomachine can release one type of signal molecules. The molecules diffuse freely in the environment and can be absorbed by another nanomachine. Because of the negative feedback inside the nanoamchine, oscillation occurs as the periodic increase and decrease of the concentration of the signal molecules. By using the proposed methodology, the synchronization of the biological nanomachines is modeled and evaluated. The influences of the distance between the biological nanomachines and the translation rate of the functional proteins on the system stability have been presented and analyzed.