A camshaft adjuster (1) for an internal combustion engine is provided, in which the relative angular position between a driving gear (2) and an output element that is allocated to the camshaft can be adjusted by hydraulically impinging pressure chambers located between an inner and outer rotor. The outer rotor and the gear ring of the driving gear (2) are joined to each other via fastening elements (15). In order to create a particularly compact camshaft adjuster (1), the fastening elements are located at least in part at a distance from the longitudinal axis of the camshaft adjuster (1) which is smaller than the external radius (35) of the pressure chambers.