The turbulent channel flow subjected to imposed harmonic oscillations is studied by theo- retical models and direct numerical simulations (DNS). A linear model proposed earlier by the present authors for the coherent perturbation Reynolds shear stress is reviewed and discussed in depth. The model includes the non-equilibrium effects during the response of the Reynolds stress to the imposed periodic shear straining, where a phase lag exists between the stress and the strain. To validate the model, the DNS results are compared with the perturbation velocity and Reynolds shear stress computed from the model. The performance of the model is good in the frequency range where quasi-static assumptions are invalid, and the viscoelastic characteris- tics of the turbulent eddies implied by the model is supported by the DNS. Attempts to improve the model are also made by incorporating in the model the DNS data. In addition, the onset of the nonlinear effects during the production of the perturbation Reynolds stresses are discussed based on the DNS data, new physical features observed from the DNS are reported.