Simulation and bisimulation are weaker than homomorphism or isomorphism,and this paper intends to give a concept stronger than simulation and weaker than bisimulation-two-way simulations.Thus,this paper firstly gives the notion of two-way simulation based on the simulation,and shows how to obtain bisimulation from two-way simulation.Secondly,it shows some properties of two-way simulation.Finally it proves some relations between two of the simulation,two-way simulation and bisimuaotin.