Motivated by N. Krasovskii＇s characterisation of exponential stability, the concept of exponential passivity is introduced. It is shown that to make a nonlinear system with factorisable high-frequency gain matrix exponentially passive via either state or output feedback, exponential minimum phaseness and invertibility conditions are necessary and sufficient. These conditions also guarantee exponential output feedback stabilisability. This result extends previous results concerning linear systems. (C)1988 Elsevier Science Ltd. All rights reserved.