Design optimization can be very time-consuming depending on the complexity of the model to be optimized. This manuscript describes the development of an adaptive response surface method for reliability-based design optimization of computation-intensive models, capable of reducing optimization times significantly. The method applied in this paper makes use of adaptive response surfaces for the elements of the considered objective function and probabilistic constraints. Because the optimization takes place on the response surface and not on the complex model itself, the number of function evaluations is reduced significantly. Higher order response models are used in combination with the adaptive approach. Additionally, the order of the interpolating functions can increase during successive iteration steps before the optimized design parameter values are achieved. The response model to be optimized is not built from a pre-defined number of design experiments, as is done usually, but is adapted and refined during the optimization routine. The proposed optimization technique is evaluated on a finite element reliability-based design optimization with multiple parameters. Copyright © 2010 John Wiley & Sons, Ltd.