Many fundamental questions in oligopoly models reduce to the analysis of the monotonicity properties of various performance measures under the model's Nash equilibrium, with respect to specific exogenously specified parameters. These strategic parameters may have an impact on the demand functions of the various competitors, their cost structures or both.In this paper, we establish first- and second-order monotonicity properties of the equilibrium prices, quantities and profits for oligopoly models with general non-linear cost functions and general dependencies of the cost and demand functions on the strategic input parameters under consideration. © 2003 Elsevier B.V. All rights reserved.