In this paper, a concentric electro-rheological clutch (ERC) is considered, embedded into a broader system: electro-hydro-aggregate (EHA) consisting of an induction motor as an electrodrive (ED) and a brake (B) as a loading machine. For ED, its dynamic moment characteristics and for B, a harmonic loading moment are taken into account. One starts from the corresponding nonlinear nondimensional dynamic model of EHA which is of the 5th order with 14 nondimensional parameters. The steady solution of the model can exhibit resonance which, due to complexity and extensiveness of the model, is very difficult to detect and analyze. Therefore, an analytical solution in the frame of the first approximation is sought, based on the method of small parameter. For this, a few simplifying assumptions are adopted (undamped system, small amplitude and frequency of load and narrow gap in ERC). Then, undamped resonance frequencies are derived and analyzed. Results are compared with resonance curves of the original and unsimplified system and further solution of the problem in question is proposed.