Petr Kurka Local return rates in substitutive subshifts (248K, Postscript) ABSTRACT. Local lower and upper return rates express the asymptotic growth of the Poincare return time of cylinders around a given point of a dynamical system. We show that in substitutive subshifts the lower (upper) local return time assumes almost everywhere its minimum (maximum) value and give an algorithm which yieldsthese two values.)