In　this　paper,　we　consider　the　partially　linear　single-index　models　with　longitudinal　data.　To　deal　with　the　variable　selection　problem　in　this　context,　we　propose　a　penalized　procedure　combined　with　two　bias　correction　methods,　resulting　in　the　bias-corrected　generalized　estimating　equation　and　the　bias-corrected　quadratic　inference　function,　which　can　take　into　account　the　correlations.　Asymptotic　properties　of　these　methods　are　demonstrated.　We　also　evaluate　the　finite　sample　performance　of　the　proposed　methods　via　Monte　Carlo　simulation　studies　and　a　real　data　analysis.