The purpose of this paper is to propose a practical method for optimum design of non-linear oil dampers with relief mechanism installed in multi-story framed building structures. The optimum design problem is formulated so as to minimize the maximum interstory drift or maximum acceleration of top-story under design earthquakes in terms of a set of relief forces subject to an inequality constraint on the maximum ratio of the damping force to the relief force and an equality constraint on the sum of relief forces of oil dampers. The proposed method to solve the optimum design problem is a successive procedure which consists of two steps. The first step is a sensitivity analysis by using nonlinear time-history response analyses, and the second step is a modification of the set of relief forces based upon the sensitivity analysis. An advanced reduction method based on static condensation of the frame and energy equivalence transformation of oil dampers is proposed and introduced into the optimum procedure to reduce the computational load. Numerical examples are conducted to demonstrate the effectiveness and validity of the proposed design method. (C) 2012 Elsevier Ltd. All rights reserved.