A camshaft phaser, including: a housing; and a phase adjustment assembly including: first and second frusto-conical shaped surfaces arranged to non-rotatably connect to a camshaft, a first one-way clutch including a third frusto-conical shaped surface; a second one-way clutch including a fourth frusto-conical shaped surface; and a displacement assembly including: a first resilient element arranged to, for an advance mode, displace the first surface in a first axial direction to non-rotatably connect the first and third surfaces and enable the second surface to rotate with respect to the housing in a first circumferential direction; and a second resilient element arranged to, for a retard mode, displace the second surface in a second axial direction to non-rotatably connect the second and fourth surfaces and enable the first surface to rotate with respect to the housing in a second circumferential direction, opposite the first circumferential direction.