Sasa Kocic Reducibility of skew-product systems with multidimensional Brjuno base flows (89K, LaTeX ) ABSTRACT. We develop a renormalization method that applies to the problem of the local reducibility of analytic skew-product flows on T^d x SL(2,R). We apply the method to give a proof of a reducibility theorem for these flows with Brjuno base frequency vectors.