cis-Decalin (2) and perylene (3) are co-enclathrated by a self-assembled M6L4-coordination cage (1) to give 1 superset(2.3) although each of them is not enclathrated. This phenomenon is termed as AND bimolecular recognition because enclathration occurs only if 2 and 3 coexist. Cage 1 also coenclathrates azulene (8) and 1,4-naphthoquinone (9) to give 1 superset(8.9). In this case, 1 superset(8)2 and 1 superset(9)2 are formed by treating 1 with 8 and 9 individually. This case is termed as OR bimolecular recognition because enclathration occurs if 8 or 9 exists. Accordingly, we have shown that the self-assembled cage 1 experiences both AND and OR bimolecular recognition.