A coupling device (1) of a switchable cam follower (2), in which a borehole (9) extends above a contact (8) for a support element in an outer lever (3) of the cam follower (2), and this borehole has a first section (10) of large diameter that starts from an outer side (11) of a crosspiece (6) on the other end (7) to which connects to a second section (12) of accordingly smaller diameter up to directly before an inner side (13) of the crosspiece (6). A smooth cylindrical coupling slide (14) is guided in a sealing manner through the second section (12), and this coupling slide projects with a sub-region (15) into the first section (10). This sub-region (15) is encompassed by a compression spring (16) that acts, on one end, against an annular end (17) formed between the sections (10, 12) and, on the other end, against a catch element (19) arranged on the lateral surface (18) of the sub-region (15). The first section (10) is closed by a thin-walled plug (20), such that a pressure space (22) for hydraulic medium is located axially between the annular end (17) of the borehole (9) and an inner side (21) of the plug (20), and for a coupled case, the coupling slide (14) can be brought into contact by hydraulic medium that can be guided into the pressure space (22) before its outer end (23) with a sub-region (25) extending on its inner end (24) with a catch surface (26) of a cross region (27) of the inner lever (4) and, for a decoupled case, the coupling slide (14) can be displaced in the direction toward the plug (20) such that it is out of contact from the catch surface (26) for a switched-off/reduced hydraulic medium pressure via the compression spring (16).