In　this　paper,　we　study　a　four-dimensional　inertial　two-nervous　system　with　delay.　By　analyzing　the　distribution　of　eigenvalues,　the　critical　value　of　zero-Hopf　bifurcation　is　obtained.　Complex　dynamic　behaviors　are　considered　when　two　parameters　change　simultaneously.　Pitchfork　and　Hopf　bifurcation　critical　lines　at　near　the　zero-Hopf　point　are　obtained　by　using　the　central　manifold　reduction　and　the　normal　form　theory.　The　bifurcation　diagram　is　given,　and　the　results　of　period-doubling　bifurcation　into　chaotic　region　in　the　inertial　two-neural　system　with　delayed　Crespi　function　are　shown.