Some discussions are given of the condensation of gasses for which the irreducible cluster integrals have approximate expressions. The case of the ring approximation was previously treated. The present paper is concerned with the generalized ring approximation and the generalized netted chain approximation, which are both better than the ring approximation. The singularity of the virial expansion, the point of condensation, the horizontal condensation line, and the two·phase separation are discussed. It is concluded that the defect in the case of the ring approximation (that is, the continuity of the slope of the isotherm at the starting point of condensation for all sufficiently low temperatures) still remains in these improved approximations, provided that we are treating the (O) ·system, i. e. the system with volume· independent cluster integrals. By making a parameter in the approximation tend to in· finity, a remark is given on the analytical properties of the condensation point in the rigorous treatment of the (0) ·system. § I. Introduction It is an interesting problem how one can, from the analytical viewpoint, develop the theory of condensation on the basis of an approximation to the ex pressions for the irreducible cluster integrals. This problem in the case of the ring approximation (which is the simplest of the useful approximations) has been discussed by one of the present authors.l)t> In the present paper, we introduce the generalized ring and generalized netted chain approximations (which are both better than the ring approximation) and discuss the above problem for these cases. In I/l in order to discuss the condensation of a gas on the basis of the ring approximation from the analytical viewpoint, an attempt was made to clarify the origin of the discrepancy between the singularity in the Born-Green-Rodriguez (BGR) theory2l of condensation [which employs an approximation equivalent to 'the ring approximation] and the singularity in Mayer's theory3l of condensation; then in I it has been shown that, if one interprets the BGR theory from the viewpoint of Mayer's theory, the singularity appearing in the BGR theory, which