Reactive sputtering is a very useful technique for fabricating oxides and other compound thin films. Very recently, we developed a technique named multi-ion-beam reactive conputtering (MI-BRECS) for preparing multi-component metal oxide thin films. In order to promote the development of this technique, it is necessary to investigate the mechanisms of thin film growth of reactive cosputtering. Based on the well-known gas kinetics, we established a fundamental model of multi-ion beam, multi-target reactive cosputtering under stable sputtering circumstances, and obtained the relationships between both the deposition rate and composition of thin films and the controllable reactive cosputtering parameters. This model reveals the essential parameters that affect the composition of thin films and the methods for controlling the deposition rate and the composition of thin films can be obtained from the model.