Tree species information is a basic variable for forest inventories. Knowledge on tree species is relevant for biomass estimation, habitat quality assessment, and biodiversity characterization. Hyperspectral data have been proven to have a high potential for the mapping of tree species composition. However, open questions remain concerning the robustness of existing classification approaches. Here, a number of classification approaches were compared to classify tree species from airborne hyperspectral data across three forest sites to identify a single approach which continuously delivers high classification performances over all test sites. Examined approaches included three feature selection methods [genetic algorithm (GA), support vector machines (SVM) wrapper, and sparse generalized partial least squares selection (PLS)] each combined with two nonparametric classifiers (SVM and Random Forest). Two further setups included classifications applied to the full hyperspectral dataset and to an image transformed with a minimum noise fraction (MNF) transformation. Results showed that SVM wrapper and the GA slightly outperformed the PLS-based algorithm. In most cases, the best classification runs involving a feature selection algorithm outperformed those incorporating the full hyperspectral dataset. However, the best overall results were obtained when using the first 10-20 components of the MNF-transformed image. Selected bands were frequently located in the visual region close to the green peak, at the chlorophyll absorption feature and the red edge rise as well as in three parts of the short-wave infrared region close to water absorption features. These findings are relevant for improving the robustness of tree species classifications from airborne hyperspectral data incorporating feature reduction techniques.