A camshaft phaser comprising first and second harmonic gear drive (HD) units disposed in back-to-back relationship. Each HD includes an elliptical wave generator (WG), a flexspline (FS) deformable by the WG, and a circular spline (CS) for engaging the FS. A dynamic spline (DS) connects the first and second FSs. The first HD is an input HD driven by an engine crankshaft via a sprocket wheel connected to the input CS. The second HD is an output HD driving an engine camshaft. The DS is meshed with both the input FS and the output FS. The phase relationship between the crankshaft and the camshaft may be changed by changing the angular relationship between the first and second WGs. Such change is effected by holding the first WG stationary and varying the angular position of the second WG via an electric motor.