In the present paper we consider a family of unobscured telescope designs with curved detectors. They are based on classical two-mirror schemes -- Ritchey-Chretien, Gregorian and Couder telescopes. It is shown that all the designs provide nearly diffraction limited image quality in the visible domain for $.4^circ times .4^circ$ field of view with the f-number of 7. We also provide a brief ghost analysis and point on special features of the systems with curved detectors. Finally, the detector surface shape obtained in each case is analyzed and its technological feasibility is demonstrated.
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