Abstract: The complicated non-linear nature of tribological system is studied on the basis of the three axioms in tribology. It is pointed out that the complicated tribological system and its behavior are characterized by time-dependence, non-linearity, randomness, chaos, and fractals of the friction and wear. Therefore, it would be helpful for further understanding the tribological fearures to apply the non-linear system theory to the researches of friction and wear behavior. In terms of the non-linear dynamic characteristics of a tribological system, the wear process consists of three newly defined stages that are different to the traditionally named ones. They include the self-organizing wear stage, the chaotic wear stage, and the unsteady wear stage. A definition of the fractal attraction factor is introduced to characterize the running-in of rubbing surface. It is supposed that mathematical model method and the fractal method could be suitable to analyzing and solving the complicated non-linear problems in a tribological system.