The two-mirror systems which are convergent and comply with |a| < 1 are discussed based on the third-order aberration theory. A general analysis on zero-coma system and zero-astigmatism system with the initial condition of zero-spherical aberration are figured out. The variety of the vertex radius of curvature R1, R2 and surface figure of primary mirror and secondary mirror with obstruction ratio a and amplification β with different aspheric coefficient are analysed. The classic systems which consisted of two mirrors are summarized.