We　get　the　estimator　of　the　link　function,　establish　the　asymptotic　properties,　and　construct　the　simultaneous　confidence　band　for　single-index　random　effects　models.　Simulation　studies　and　real　data　set　are　presented　to　evaluate　the　performance　of　the　proposed　method.　(C)　2013　Elsevier　B.V.　All　rights　reserved.