In　this　paper,　we　consider　the　partially　linear　single-index　models　with　longitudinal　data.　We　propose　the　bias-corrected　quadratic　inference　function　(QIF)　method　to　estimate　the　parameters　in　the　model　by　accounting　for　the　within-subject　correlation.　Asymptotic　properties　for　the　proposed　estimation　methods　are　demonstrated.　A　generalized　likelihood　ratio　test　is　established　to　test　the　linearity　of　the　nonparametric　part.　Under　the　null　hypotheses,　the　test　statistic　follows　asymptotically　a　chi(2)　distribution.　We　also　evaluate　the　finite　sample　performance　of　the　proposed　methods　via　Monte　Carlo　simulation　studies　and　a　real　data　analysis.　(C)　2013　Elsevier　Inc.　All　rights　reserved.