Abstract: Two kinds of boundry curves, I.e. boundary curve for conjugation and boundary curve for curvatural interference, are discussed in this paper. Five types of singular solutions in conjugate curvatures, I. E, cusp-point type, surf acial-contact type, indefinite type, stationary type and hypo-surfacial-contact type, are denominated and studied. Furthermore, two kinds of complementary conjugate surfaces, which correspond with the two kinds of boundary curves, are commented. Finally, a new analytical process for the determination of the characteristics of a surface in conjugation, I. E, the conjugatiou-analysis, is described in this paper.