The presenter has recently been exploring the accurate computation of the stationary distribution for finite Markov chains based upon the Grassman, Taksar and Heyman (GTH) algorithm ([1]) with further extensions of this procedure, based upon the ideas of Kohlas ([2]), for finding the mean first passage time matrix. The methods are numerically stable as they do not involve subtraction. In addition, a number of perturbation techniques, where the rows of the transition matrix are sequentially updated, are also considered for computing these quantities. These techniques, together with some standard techniques using matrix inverses and generalized inverses, are compared for accuracy, using some test problems from the literature. References: [1} Grassman W.K., Taksar M.I., and Heyman D.P., Regenerative analysis and steady state distributions for Markov chains, Oper. Res. 33, (1985), 1107-1116. [2] Kohlas J. Numerical computation of mean first passage times and absorption probabilities in Markov and semi-Markov models, Zeit fur Oper Res, 30, (1986), 197-207.