In　this　article　local　empirical　likelihood-based　inference　for　a　varying　coefficient　model　with　longitudinal　data　is　investigated.　First,　we　show　that　the　naive　empirical　likelihood　ratio　is　asymptotically　standard　chi-squared　when　undersmoothing　is　employed.　The　ratio　is　self-scale　invariant　and　the　plug-in　estimate　of　the　limiting　variance　is　not　needed.　Second,　to　enhance　the　performance　of　the　ratio,　mean-corrected　and　residual-adjusted　empirical　likelihood　ratios　are　recommended.　The　merit　of　these　two　bias　corrections　is　that　without　undersmoothing,　both　also　have　standard　chi-squared　limits.　Third,　a　maximum　empirical　likelihood　estimator　(MELE)　of　the　time-varying　coefficient　is　defined,　the　asymptotic　equivalence　to　the　weighted　least-squares　estimator　(WLSE)　is　provided,　and　the　asymptotic　normality　is　shown.　By　the　empirical　likelihood　ratios　and　the　normal　approximation　of　the　MELE/WLSE,　the　confidence　regions　of　the　time-varying　coefficients　are　constructed.　Fourth,　when　some　components　are　of　particular　interest,　we　suggest　using　mean-corrected　and　residual-adjusted　partial　empirical　likelihood　ratios　to　construct　the　confidence　regions/intervals.　In　addition,　we　also　consider　the　construction　of　the　simultaneous　and　bootstrap　confidence　bands.　A　simulation　study　is　undertaken　to　compare　the　empirical　likelihood,　the　normal　approximation,　and　the　bootstrap　methods　in　terms　of　coverage　accuracies　and　average　areas/widths　of　confidence　regions/bands.　An　example　in　epidemiology　is　used　for　illustration.