The twin rotor damper (TRD), an active mass damping device, is used for the vibration control of a multi-degree-of-freedom (MDOF) system of oscillators. A single TRD unit consists of two eccentric control masses rotating about two parallel axes. In its principle mode of operation, the continuous rotation mode (CRM), the control masses rotate with a constant angular velocity in opposite directions; producing a monofrequent harmonic control force in an energy and power efficient manner. Extensive research has shown the effectiveness of the TRD in the CRM for systems with a single dominate mode of vibration. In this paper, the application of a single and multiple TRD units operating in the CRM is investigated for the control of a MDOF system of oscillators. The influence of the monofrequent control force produced by the TRD on the MDOF system of oscillators is investigated analytically. Subsequently, the analysis is inverted and the influence of the MDOF system of oscillators on the TRD is studied, in particular its power efficiency and damping performance. Finally, the power efficiency and damping performance of the TRD for the control of a system with two modes of vibration is analytically compared with that of a conventional active mass damping (CAMD) device. It is shown that in most cases, the TRD achieves greater damping performance in a more power efficient manner than a conventional active mass damper of similar size and mass.