All rotating systems are subjected to residual unbalance forces that are proportional to speed squared. Systems that operate close to the critical speed and have low damping can generate destructive vibrations. Dynamic vibration absorbers are simple devices attached to a mechanical structure (the primary system) to reduce vibrations and noise levels and are extensively used in non-rotating systems. This study addresses the design of viscoelastic vibration absorbers for rotating systems. The primary system is modeled using modal parameters obtained in the frequency domain of the state-space representation. Using a methodology that has a more general application, the compound system (the primary system and absorbers) is represented in a modal subspace of the primary system state space. In this modal subspace, the optimal design of the dynamic viscoelastic absorbers is performed using an optimization algorithm. The objective function to be minimized is defined as the Euclidean norm of the vector composed of the maximal absolute values of the principal coordinates. The absorbers are attached to a floating bearing located away from a nodal point. Numerical and experimental results are presented and discussed.