Recent　reports　show　that　projection　neural　networks　with　a　low-dimensional　state　space　can　enhance　computation　speed　obviously.　This　paper　proposes　two　projection　neural　networks　with　reduced　model　dimension　and　complexity　(RDPNNs)　for　solving　nonlinear　programming　(NP)　problems.　Compared　with　existing　projection　neural　networks　for　solving　NP,　the　proposed　two　RDPNNs　have　a　low-dimensional　state　space　and　low　model　complexity.　Under　the　condition　that　the　Hessian　matrix　of　the　associated　Lagrangian　function　is　positive　semi-definite　and　positive　definite　at　each　Karush-Kuhn-Tucker　point,　the　proposed　two　RDPNNs　are　proven　to　be　globally　stable　in　the　sense　of　Lyapunov　and　converge　globally　to　a　point　satisfying　the　reduced　optimality　condition　of　NP.　Therefore,　the　proposed　two　RDPNNs　are　theoretically　guaranteed　to　solve　convex　NP　problems　and　a　class　of　nonconvex　NP　problems.　Computed　results　show　that　the　proposed　two　RDPNNs　have　a　faster　computation　speed　than　the　existing　projection　neural　networks　for　solving　NP　problems.