We　consider　the　fixed　effects　panel　data　single-index　model.　For　estimation　of　the　link　function　and　the　index　parameter,　the　local　linear　smoothing　and　the　least　squares　method　are　used.　We　also　propose　a　test　for　the　presence　of　the　fixed　effects.　Finite　sample　performances　are　illustrated　using　simulations.　(C)　2013　Elsevier　B.V.　All　rights　reserved.