  We study spectral properties of a system of two quantum particles on an
integer lattice with a bounded short-range two-body interaction, in an external
random potential field $V(x,\omega)$ with independent, identically distributed
values. The main result is that if the common probability density $f$ of random
variables $V(x,\omega)$ is analytic in a strip around the real line and the
amplitude constant $g$ is large enough (i.e. the system is at high disorder),
then, with probability one, the spectrum of the two-particle lattice
Schroedinger operator $H(\omega)$ (bosonic or fermionic) is pure point, and all
eigen-functions decay exponentially. The proof given in this paper is based on
a refinement of a multiscale analysis (MSA) scheme proposed by von Dreifus and
Klein, adapted to incorporate lattice systems with interaction.
