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This paper evaluates nonlinear retrieval methods to derive atmospheric properties from hyperspectral infrared sounding spectra, with emphasis on the retrieval of temperature, humidity, and ozone atmospheric profiles. We concentrate on the Infrared Atmospheric Sounding Interferometer (IASI) onboard the MetOp-A satellite data for the future Meteosat Third Generation Infrared Sounder (MTG-IRS). The methods proposed in this work are compared in terms of both accuracy and speed with the current MTG-IRS L2 processing concept, which processes MetOp-IASI and proxy MTG-IRS data. The official chain consists of a principal component extraction, typically referred to as empirical orthogonal functions (EOF) and a subsequent canonical linear regression. This research proposes the evaluation of some other methodological advances considering: 1) other linear feature extraction methods instead of EOF, such as partial least squares; and 2) the linear combination of nonlinear regression models in the form of committee of experts. The nonlinear regression models considered in this work are artificial neural networks and kernel ridge regression as nonparametric multioutput powerful regression tools. Results show that, in general, nonlinear models yield better results than linear retrieval for both MetOp-IASI and MTG-IRS synthetic and real data. Averaged gains throughout the column of +1.8 K and +2.2 K are obtained for temperature profile estimation from MetOp-IASI and IRS data, respectively. Similar gains are obtained for the estimation of dew point temperatures. In both variables, these improvements are more noticeable in lower atmospheric layers. The combination of models makes the retrieval more robust, improves the accuracy, and decreases the estimated bias. The nonlinear statistical approach is successfully compared to optimal estimation (OE) in terms of accuracy, bias and computational cost. These results confirm the potential of statistical nonlinear inversion techniques for the- retrieval of atmospheric profiles.