This paper considers multivariate local linear least squares estimation of panel data models when fixed effects are present. One-step estimation of the local marginal effect is of prime interest. A within-group nonparametric estimator is developed, where the fixed effects are eliminated by subtracting individual-specific locally weighted time average, i.e., the local-within-transformation. It is shown that the local-within-transformation-based estimator satisfies the standard properties of the local linear estimator. In comparison, nonparametric estimators based on the conventional (global) within-transformation or first difference result in estimators which are biased, even in large samples. The new estimator is used to examine the nonlinear relationship between income and nitrogen-oxide level (i.e., the environmental Kuznets curve) based on U.S. state-level panel data.