Abstract: In this paper, the existence of closed orbits for the biochemical reaction model dx/dt=1-xⁿy²,dy/dt=a(xⁿy²-y) is discussed, where n is a positive integer and x≥0,y≥0,a>0 We also point out that the equation has no dosed orbits or has stable limit cycles arising from Hopf bifurcations under a certain condition of a.