We show how atomic force microscopy techniques based on contact resonance (CR) can be used to measure the viscoelastic loss tangent tan delta of polymeric materials. The method does not require intermediate calculation of loss and storage moduli, calibration measurements, or use of the conventional CR tip shape parameter. We present the method's physical concepts and sensitivity calculations for typical experimental parameters. In addition, CR experiments were performed on four homogeneous polymer samples (polystyrene, high-density polyethylene, and two commercial photostress polymers) with tan (5 in the range from approximately 0.02 to 0.2. Results compare favorably to those obtained by microscale dynamic nanoindentation and macroscale dynamic mechanical analysis. These results show the potential of CR modes for nanoscale viscoelastic measurements of polymers and biomaterials.