Theoretical and practical aspects are examined that relate to the development of multiple-array telescope systems that offer aspheric correction with the fewest components. The paper compares two designs and investigates the effects of different relative apertures for the primary mirror and different system lengths on the symmetry and order of aberrations generated by the eccentric aspheric. The first approach involves the use of Mersenne collecting telescopes, and the second configuration is based on four-mirror telescopes. It is shown that the use of special surfaces for decentered aspheric correction is limited and that pupil matching is important in the shared-symmetry array systems. Three- and five-mirror designs are analyzed and found to be diffraction-limited for a field of up to 60 arcmin, and reference is made to the complex calculations for determining the decentered asphericity.