This paper provides an approach to estimation and inference for nonlinear conditional mean panel data models, in the presence of cross-sectional dependence. We modify Pesaran's (Econometrica, 2006, 74(4), 967-1012) common correlated effects correction to filter out the interactive unobserved multifactor structure. The estimation can be carried out using nonlinear least squares, by augmenting the set of explanatory variables with cross-sectional averages of both linear and nonlinear terms. We propose pooled and mean group estimators, derive their asymptotic distributions, and show the consistency and asymptotic normality of the coefficients of the model. The features of the proposed estimators are investigated through extensive Monte Carlo experiments. We also present two empirical exercises. The first explores the nonlinear relationship between banks' capital ratios and riskiness. The second estimates the nonlinear effect of national savings on national investment in OECD countries depending on countries' openness.