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Nineteen classical superintegrable systems in two-dimensional non-Euclideanspaces are shown to possess hidden symmetries leading to their linearization.They are the two Perlick systems [A. Ballesteros, A. Enciso, F.J. Herranz andO. Ragnisco, Class. Quantum Grav. 25, 165005 (2008)], the Taub-NUT system [A.Ballesteros, A. Enciso, F.J. Herranz, O. Ragnisco, and D. Riglioni, SIGMA 7,048 (2011)], and all the seventeen superintegrable systems for the four typesof Darboux spaces as determined in [E.G. Kalnins, J.M. Kress, W. Miller, P.Winternitz, J. Math. Phys. 44, 5811--5848 (2003)].

Superintegrable systems in non-Euclidean plane: hidden symmetries leading to linearity