Journal article: Local perturbation) methods compute solutions in one point and tend to deliver far lower accuracy levels than global solution methods. We develop a hybrid method that solves for some policy functions locally (using a perturbation method) and that solves for the other policy functions globally (using closed-form expressions and a numerical solver). We applied our hybrid method to solve large-scale RBC models used in the comparison analysis of Kollmann et al. (J Econ Dyn Control 35:186-202, 2011b). We obtain more accurate solutions than those produced by any other (either local or global) solution method participating in that comparison. Our running time is a few seconds.