Two kinds of game models based on viability theory (non-cooperative game model and cooperative game model) and the existence of equilibrium are studied. The viability theory is implanted into non-cooperative game and cooperative game models, and two new game models are constructed, and the strong (weak) equilibria of non-cooperative game and strong (weak) equilibria of cooperative game are defined. Under certain conditions, four existence theorems of strong (weak) equilibria are obtained. This work broadens the research scope of game theory theoretically and has certain practical significance in application.