  We consider a time-homogeneous Markov chain $X_n$, $n\ge0$, valued in ${\bf
R}$. Suppose that this chain is transient, that is, $X_n$ generates a
$\sigma$-finite renewal measure. We prove the key renewal theorem under
condition that this chain has asymptotically homogeneous at infinity jumps and
asymptotically positive drift.
