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This paper analyzes outlier detection for functional data by means of functional depths, which measures the centrality of a given curve within a group of trajectories providing center-outward orderings of the set of curves. We give some insights of the usefulness of looking for outliers in functional datasets and propose a method based in depths for the functional outlier detection. The performance of the proposed procedure is analyzed by several Monte Carlo experiments. Finally, we illustrate the procedure by finding outliers in a dataset of NOx (nitrogen oxides) emissions taken from a control station near an industrial area.