  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.
