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 Zero-Hopf bifurcation in nuclear spin generator system Renxiang Shi,Jiang Yu Keywords:averaging method; nuclear spin generator; limit cycle; zero-Hopf bifurcation Abstract: By computing we obtain that $P_{1}(0,0,1)$ is a zero-Hopf equilibrium point of nuclear spin generator system. We prove that there exist two families of nuclear spin generator system which has the zero-Hopf equilibrium point $P_{1}(0,0,1)$. Furthermore we prove that a limit cycle bifurcated from $P_{1}(0,0,1)$ by averaging method of one order and second order respctively.