In　this　article,　a　second-order　derivative　neural　network　approach　is　proposed　for　microwave　device　modeling　to　address　the　situation　where　not　only　the　input-output　relationship　but　also　its　high-order　derivatives　need　to　be　accurately　modeled.　In　this　method,　the　proposed　overall　model　includes　the　original　neural　network,　the　adjoint　model,　and　a　second　order　derivative　model.　The　new　formulation　and　new　sensitivity　analysis　technique　of　the　second-order　derivatives　of　the　neural　network　are　derived.　New　formulations　are　deduced　for　second　order　sensitivity　modeling　of　multilayer　neural　networks　with　three　layers　and　any　number　of　hidden　neurons.　To　accelerate　the　training　process　of　the　second-order　derivative　model,　a　third-order　derivative　sensitivity　analysis　is　formulated　to　train　the　second-order　derivative　model.　The　proposed　technique　can　efficiently　and　accurately　represent　the　input-output　relationship　with　its　high-order　derivatives.　A　gallium　arsenide　(GaAs)　metal-semiconductor-field-effect　transistor　(MESFET)　and　a　measured　2　x　50　mu　s　gatewidths　GaAs　Pseudomorphic　high-electron-mobility　transistor　(pHEMT)　examples　are　used　to　validate　the　proposed　technique.