Abstract: The importance,undesired situation of development of tribology and the reasons are described. Problems come from insufficient study on the theory system and method system in tribology, which can match the definition and nature of tribology and can support an independent development of tribology. Since 1966 the methodology of investigating tribology has not been improved from that for investigating friction, wear and lubrication of a single tribo pair. It is found that there are three axioms in tribology. They are discussed in detail in connection with examples. Namely,axiom I:the tribological behavior is system dependent that single surfaces or medium substance cannot realize any tribological behavior;axiom II:The property of tribo elements and the systems with tribo elements are time dependent;axiom III: Tribological behaviors are the results of strong coupling of many behaviors of other disciplines, such as mechanics, chemistry, heat transfer, material science, electronics and theory of control. Tribology is the science, which provides theories and technology to describe and control the pattern of coupling between behaviors under tribological condition. No other discipline can meet such a need. A series of theories and lemmas has been deduced from the axioms. It has also been suggested that the state equations and output equations, which are familiar in control engineering can be used to describe the property of a tribo system. It is expected that the axioms,theories, lemmas, concepts and methods given could be used as guidance in establishing the theory system and method system of tribology.