  In this article we obtain asymptotic formulas for the eigenvalues and
eigenfunctions of the non-self-adjoint operator generated in space of
vector-functions by the Sturm-Liouville equation with m by m matrix potential
and the boundary conditions whose scalar case (m=1) are strongly regular. Using
these asymptotic formulas, we find a condition on the potential for which the
root functions of this operator form a Riesz basis.
