In　this　paper,　we　generalize　the　single-index　models　to　the　scenarios　with　random　effects.　The　introduction　of　the　random　effects　raises　interesting　inferential　challenges.　Instead　of　treating　the　variance　matrix　as　the　tuning　parameters　in　the　nonparametric　model　of　Gu　and　Ma　(2005),　we　propose　root-n　consistent　estimators　for　the　variance　components.　Furthermore,　the　single-index　part　in　our　model　avoids　the　curse　of　dimensionality　and　makes　our　model　simpler.　The　variance　components　also　cannot　be　treated　as　nuisance　parameters　and　are　canceled　in　the　estimation　procedure　like　Wang　et　al.　(2010).　A　new　set　of　estimating　equations　modified　for　the　boundary　effects　is　proposed　to　estimate　the　index　coefficients.　The　link　function　is　estimated　by　using　the　local　linear　smoother.　Asymptotic　normality　is　established　for　the　proposed　estimators.　Also,　the　estimator　of　the　link　function　achieves　optimal　convergence　rate.　These　results　facilitate　the　construction　of　confidence　regions　and　hypothesis　testing　for　the　parameters　of　interest.　Simulations　show　that　our　methods　work　well　for　high-dimensional　p.　(c)　2011　Elsevier　B.V.　All　rights　reserved.