In　this　paper,　we　propose　simultaneous　confidence　bands　for　the　nonparametric　link　function　in　single-index　models　in　the　presence　of　a　nuisance　index　parameter.　We　establish　the　asymptotic　properties　for　the　link　function　and　its　derivative　that　allow　simultaneous　confidence　bands　for　various　inference　tasks.　In　addition,　we　propose　an　adaptive　Neyman　test　statistic　for　testing　the　linearity　of　the　link　function.　We　then　conduct　simulation　studies　to　evaluate　the　performance　of　the　proposed　method,　and　apply　them　to　two　data　sets　for　illustration.