In　this　paper,　fractional-order　recurrent　neural　network　models　with　Caputo　Derivative　are　investigated.　Firstly,　we　mainly　focus　our　attention　on　Hopf　bifurcation　conditions　for　commensurate　fractional-order　network　with　time　delay　to　reveal　the　essence　that　fractional-order　equation　can　simulate　the　activity　of　neuron　oscillation.　Secondly,　for　incommensurate　fractional-order　neural　network　model,　we　prove　the　stability　of　the　zero　equilibrium　point　to　show　that　incommensurate　fractional-order　neural　network　still　converges　to　zero　point.　Finally,　Hopf　bifurcation　conditions　for　the　incommensurate　fractional-order　neural　network　model　are　first　obtained　using　bifurcation　theory　based　on　commensurate　fractional-order　system.