  In this article we obtain the asymptotic formulas for the eigenvalues and
eigenfunctions of the self-adjoint operator generated by a system of
Sturm-Liouville equations with summable coefficients and the quasiperiodic
boundary conditions. Then using these asymptotic formulas, we find the
conditions on the potential for which the number of gaps in the spectrum of the
Hill's operator with matrix potential is finite.
