Vibration isolation is well recognized as an effective mitigation strategy for acceleration-sensitive equipment subjected to earthquake. In the present paper, an equipment isolation system with nonlinear hysteretic behaviour is proposed and a methodology for the optimal design is developed. An integrable constitutive model, derived from the mathematical Duhem hysteresis operator, is adopted for the isolation system. The optimization procedure is defined through a dual-criteria approach that involves a transmissibility criterion combined with an energy performance criterion: the former consists in limiting the absolute acceleration of the isolated equipment below an allowable threshold value; the latter, in maximizing the ratio between the energy dissipation due to hysteresis and the input energy to reduce the isolator displacements. The seismic effectiveness of the nonlinear hysteretic isolation system is numerically investigated under natural accelerograms with different frequency content and increasing levels of excitation. Both ground-mounted and floor-mounted equipment items are considered in the analyses; in the second case, the dynamic interaction between the equipment and its supporting structure is taken into account in the design of the isolation system, and its effects on the isolation performance and the structural response are discussed. Comparisons in terms of effectiveness and robustness with a linear isolation system with viscoelastic behaviour are eventually provided. Copyright © 2013 John Wiley & Sons, Ltd.