Abstract: An autocatalytic reaction model X+2Y→3Y, Y+Z→2Z, Y→P, in a CSTR is put forward to model the phenomena of birhythum and tristability in isothermal, homogeneous chemical systems. Numerical simulations show that, under the proper values of the parameters, system may evolve to and remain at two or three different asymptotic states under same parameter's values but different initial values of X, Y and Z. In some cases, two of these asymptotic states are oscillatory, as shown in Fig.1. This is the phenomenon of birhythum. The stability of these asymptotic states are discussed. Some of them are not strickly stable but might be observed experimentally in chemical systems. It′s implications to the problem of biological evolution is also discussed.