Abstract: System thinking has arisen since the early stage of tribology study. No significant development in the overall theory of tribology results no significant development in the system theory and modeling of tribo-systems. Based on the three axioms of tribology and by integrating the general system theory with engineering system analysis, the function and the composition of tribo-systems are investigated. It is concluded that tribo-systems provide for moving systems a motion guarantee function which keeps all components in a moving system with definite relative motions. The function is implemented by all tribo-pairs in the system together with several sub-systems to support tribo-pairs working reliably. Therefore tribo-systems are the sub-systems of moving systems abstracted from which for investigating tribology behaviors therein. The motion guarantee function determines that there must be parameters concerning with motions of components in the system state parameter sets and these parameters are very important for tribology study. The structure of tribo-systems is on history depending and with state variation following. Therefore tribo-systems are time-variable and non-linear. Fortunately such two kinds of variations are with different time scales, of very long period and of very short period in comparison with the former. It founds a theoretical base to establish an algorithm of piecewise stationarized and piecewise linearized with different time scales. Most simplifications taken previously in structure modeling to avoid unintegrable can then be considered. Many factors simplified before are important and cannot be ignored for tribo-systems. Simultaneously the behaviors of different disciplines can then be coupled and applied together on the tribo-system through a history depending and state following structure as well in modeling. A tribo-system including cylinder liner – piston skirt pair, conrod big and small head bearings and crank shaft bearings of IC engines is given as a computational example.