The geometrical optics for constructing the reflector of a non-parabolic asymmetrical solar concentrator are reviewed. A prototype concentrator of this kind has been constructed with a concentration ratio of 4.07 and a theoretical optical efficiency eta/sub 0/ = 0.67. Standard performance tests on such a concentrator indicate a heat-loss coefficient U = 4.35 Wm/sup -2/ /sup 0/C/sup -1/ and a heat-extraction efficiency factor F = 0.92. 12 references.