A method of global stability analysis is proposed for a feedback system with dead-zone nonlinearities. Using a global property that the output of a saturation function is bounded, the bound on the input to the saturation function is estimated using the L-infinity norm of a linear subsystem. The feedback system can be treated as a feedback system with a narrower sector bound using this method, and a sharper global stability condition is obtained by applying the circle or Popov criterion to the system. (C) 2016 Elsevier Ltd. All rights reserved.