The angular-momentum detection of the magnetic resonance is theoretically examined. The modified Bloch equations are rcsolved in order to obtain the power absorption and the torque on the sample at low d.c. magnetic fields in the presence of strong linearly polarized r.f. fields. The Bloch-Siegert effect and a saturation shift, due to superposition of the absorptions lines of the two rotating fields, arc directly derived from the equations. Many-photon absorptions, line shapes and shifts are examined. The differences between two different methods of detection (detection of absorbed power and detection of angular momentum) are emphasized.