We derive a generalized functional method of nonimaging optical design, applicable in the case of axisymmetric or translationally symmetric geometries utilizing extended sources and multiple reflective and/or refractive optical surfaces. Design methods are described for generation of a specified intensity distribution as a function of angle or a specified irradiance distribution as a function of position along the shape profile of an aspheric target surface. A related method is presented for the design of two successive optical surfaces that transform a given source distribution into either two specified irradiance distributions on successive target surfaces or a specified irradiance distribution and a specified intensity distribution.