A linear convolution scheme involving first-order (linear) kernels for linear bridge aerodynamics is first reviewed and the significance of the selection of proper input parameters is emphasized. Following the concept of nonlinear indicial response function, the linear convolution scheme is extended to the nonlinear convolution scheme involving higher-order (nonlinear) kernels for the treatment of nonlinear bridge aerodynamics using a "peeling-an-onion" type procedure. Utilizing an impulse function as input, a comprehensive kernel identification scheme is developed. A numerical example of a long-span suspension bridge is investigated to verify the fidelity of the proposed nonlinear convolution scheme. (C) 2013 Elsevier Ltd. All rights reserved.