{For chemical systems involving both fast and slow-scales, stiffness presents challenges for efficient stochastic simulation. Two different avenues have been explored to solve this problem. One is the slow-scale stochastic simulation (ssSSA) based on the stochastic partial equilibrium assumption. The other is the tau-leaping method. In this paper, we propose a new algorithm, the slow-scale tau-leaping method, which combines some of the best features of these two methods. Numerical experiments are presented which illustrate the effectiveness of this approach. (C) 2008 Elsevier B.V. All rights reserved.}