Abstract. An important requirement of numerical methods for the integration of nonlinear stiff initial value problems is B-stability. In many applications it is also convenient to use splitting methods to take advantage of the special structure of the differential operator that defines the model. The purpose of this paper is to provide a necessary and sufficient condition for the B-stability of additive Runge-Kutta methods. We also present a family of B-stable fractional step Runge-Kutta methods.