The paper investigates hydraulic wave propagation phenomena through hydraulic circuits of power transmission systems by means of numerical approaches. The actuation circuit of a Dual-Clutch Transmission (DCT) power transmission system supplied by a Gerotor pump is analyzed. A steady state approach is adopted to detect resonance phenomena due to Gerotor design parameters and circuit lengths, while one-dimensional numerical models are implemented to predict the pressure oscillations through the hydraulic ducts for the whole pump operating domain. CFD-1D pipelines are adopted to address the pressure oscillation behavior through the hydraulic pipeline, while spectral maps and order tracking techniques are used to evaluate their fluctuation intensity in function of the pump speed rate. The numerical models are validated with experimental tests performed on an ad hoc test rig for power transmission systems and a good match is found between the numerical and the experimental results. Pump design parameters as well as hydraulic accumulators and resonators are numerically investigated to quantitatively evaluate their improvement on the circuits’ hydro-dynamic behavior. Furthermore, simplified numerical models are implemented to investigate the frequency response behavior of the hydraulic circuits by means of linear analysis. This approach resulted to be particularly effective for the prediction of the resonance frequencies location, and it can be adopted as an optimization tool since significant simulation time can be saved. Finally, the performance of the circuits operating with an eco-friendly fluid is evaluated numerically and the results are compared with the ones obtained with a traditional petroleum-based oil.