Gillespie's algorithm, also known as the Stochastic Simulation Algorithm (SSA), is an exact simulation method for the Chemical Master Equation model of well-stirred biochemical systems. However, this method is computationally intensive when some fast reactions are present in the system. The tau-leap scheme developed by Gillespie can speed up the stochastic simulation of these biochemically reacting systems with negligible loss in accuracy. A number of tau-leaping methods were proposed, including the explicit tau-leaping and the implicit tau-leaping strategies. Nonetheless, these
schemes have low order of accuracy. In this thesis, we investigate tau-leap strategies which achieve high accuracy at reduced computational cost. These strategies are tested on several biochemical systems of practical interest.