  In this paper, we consider a general class of two-time-scale Markov chains
whose transition rate matrix depends on a parameter $\lambda>0$. We assume that
some transition rates of the Markov chain will tend to infinity as
$\lambda\rightarrow\infty$. We divide the state space of the Markov chain $X$
into a fast state space and a slow state space and define a reduced chain $Y$
on the slow state space. Our main result is that the distribution of the
original chain $X$ will converge in total variation distance to that of the
reduced chain $Y$ uniformly in time $t$ as $\lambda\rightarrow\infty$.
