  This is one of results from our program of massive simulations of close
encounters for all nearby stars. Epsilon Eridani is an extremely interesting
star having one confirmed planet and multiple asteroid and debris belts. It
should have a quite massive Oort cloud as well. Deltorn et al. searched for
past Nemesis encounters of $\varepsilon$ Eri. In this paper we show that,
according to current astrometric data, an other famous nearby star Luyten
726-8AB (=BL/UV Ceti) will pass at $\lesssim$ 0.93 ly from Epsilon Eridani in
$\approx$ 31.5 kyr. So, it will probably pierce through the outer part of the
hypothetical Oort cloud of $\epsilon$ Eri. BL/UV Ceti has only about 20 percent
of the solar mass. Nevertheless, it could influence directly some long-period
comets of Epsilon Eridani. The duration of mutual transit of two star systems
within 1 ly from each other is $\gtrsim$ 4.6 kyr. Our simulations show that
stellar encounters within 1 ly might be more frequent than previously thought.
It could explain Proxima's peculiar trajectory with respect to $\alpha$ Cen AB
or even Sedna's trajectory in the solar system.

Solar and Stellar Astrophysics