With the charged-particle momentum resolving 4π-detector SAPHIR at the electron stretcher ring ELSA in Bonn the photoproduction of η- and η′-mesons off the proton were measured from threshold up to 2.64 GeV photon energy. The tagger and the method of analysis are shortly described. Three track events from the decays γp→pη →pπ + π - π 0 /γ and γp→pη′ →pπ + π - η are investigated. From about 5×10 6 hadronic 3-prong events of the runs in 1997 and 1998 about 13800 η- and 4200 η′-events could be selected. The data were analyzed in terms of cross sections and angular distributions. The results on η-mesons extend previous data to much higher energies and present new interesting phenomena. For the new 3-prong η′-data the absolute normalisation is still lacking but the shapes of the differential cross sections and of the excitation function are consistent with those of the previous analysis of 5-prong events. At higher energies the data are quite well reproduced by a model describing the exchange of Regge-trajectories in the t-channel while at lower energies the contribution of a S 11 (1900) nucleon resonance in the s-channel is indicated.