A subclass of the class of geometrically infinitely divisible distributions which is a generalization of geometrically stable distributions is presented. The author establishes four theorems. In the first one, a necessary and sufficient condition for a distribution to be generalized geometrically stable (GGS) is given. In the second theorem it is shown that the GGS random variable has the same distribution as the geometric sum of iid random variables with certain characteristic functions. The remaining theorems provide the analogy of Lévy's canonical representation for a characteristic function of the GGS distribution and render concrete what kind are the GGS distributions. The proofs are based on Theorem 2 in \textit{L. B. Klebanov}, \textit{G. M. Maniya} and the reviewer, Teor. Veroyatn. Primen. 29, No.4, 757-760 (1984; Zbl 0565.60014); English translation in Theory Probab. Appl. 29, 791-794 (1985). Unfortunately, there are some inaccuracies in the paper which impede its reading.