  Oeljeklaus-Toma manifolds are complex non-K\"ahler manifolds constructed by
Oeljeklaus and Toma from certain number fields. These manifolds generalize
Inoue surfaces of type $S_m$. In this work it is shown that Oeljeklaus-Toma
manifolds could not contain any compact complex submanifolds of dimension 2
(surfaces) except Inoue surfaces.
