Considerable effort has been devoted recently to the design, analysis, fabrication, and testing of spherical Schwarzschild microscopes for soft x-ray applications in microscopy and projection lithography. The spherical Schwarzschild microscope consists of two concentric spherical mirrors configured such that the third-order spherical aberration and coma are zero. Because multilayers are used on the mirror substrates for soft x-ray applications, it is desirable to have a small number of reflecting surfaces in the microscope. In order to reduce the microscope aberrations and increase the field of view, generalized mirror surface profiles have been considered in this study for a two-mirror microscope. Based on incoherent, sine wave modulation transfer function (MTF) calculations, the object plane resolution of a 20x microscope has been analyzed as a function of the object height and numerical aperture (NA) of the primary for several spherical Schwarzschild, conic, and aspherical reflecting two-mirror microscope configurations. The ultimate resolution of an aspherical, two-mirror microscope appears to be about 200 Å when using 100-Å radiation. Better resolution can be achieved when shorter wavelength radiation is used.