A better and more practical fermentation method was sought out to produce a biochemically valuable compound, 3'',5''-cyclic adenylic acid, from adenosine, adenine, inosine, hypoxanthine, 5amino-4-imidazolecarboxamide-riboside, 5-amino-4imidazolecarboxamide, succinyl adenosine, and succinyl adenine, by cultivating aerobically under suitable conditions a strain of micro-organisms belonging to one of Corynebacterium murisepticum No. 7 (ATCC 21374), a new species of Arthrobacter, No. 11 (ATCC 21375) and a new species of Microbacterium, No. 205 (ATCC 21376), and being capable of producing said acid from the above-named compounds, in a medium which contains, other than at least one of said compounds, suitable carbon sources, nitrogen sources and other inorganic substances. Then, 3'',5''-cyclic adenylic acid thus formed and accumulated in said medium was further purified by means of charcoal and appropriate ion exchange resins and the like.