The authors develop a new approach to model the optimal policies of machine replacement under technological change. They consider a single-machine replacement problem in continuous time and reduce it to a nonlinear integral equation for the variable optimal service life of machine. A qualitative analysis of this equation leads to new dynamic properties of the optimal replacement. A numeric example on industrial data about car replacement illustrates obtained analytic results. It confirms the validity and robustness of the developed technique and demonstrates its practical advantages. © 2008 Elsevier B.V. All rights reserved.