  We prove an analog of the classical Zero-One Law for both homogeneous and
nonhomogeneous Markov chains (MC). Its almost precise formulation is simple:
given any event $A$ from the tail $\sigma$-algebra of MC $(Z_n)$, for large
$n$, with probability near one, the trajectories of the MC are in states $i$,
where $P(A|Z_n=i)$ is either near $0$ or near $1$. A similar statement holds
for the entrance $\sigma$-algebra, when $n$ tends to $-\infty$. To formulate
this second result, we give detailed results on the existence of nonhomogeneous
Markov chains indexed by $\mathbb Z_-$ or $\mathbb Z$ in both the finite and
countable cases. This extends a well-known result due to Kolmogorov. Further,
in our discussion, we note an interesting dichotomy between two commonly used
definitions of MCs.
