Polymers in a liquid crystalline nematic phase exhibit complex theological behavior. Under steady shear flow and in homogeneous conditions, different regimes have been theoretically predicted, and in some cases experimentally observed. In particular, periodic and even aperiodic regimes have been theoretically predicted. Sustained periodic stress responses have been recently measured on a lyotropic sample of PBG in m-cresol. The natural oscillating behavior, known as tumbling or wagging regimes, can give rise to a number of resonance phenomena when the system is forced by proper periodic flow. We will show that frequency-locking phenomena are predicted under such conditions, and that the Arnol'd tongues can be used to discriminate unforced periodic behavior. The nematic polymer is modeled by a simplified equation derived from a rigid rod model. (C) 2003 The Society of Rheology.