  We consider the differential system $y'-x^{-1}Ay-q(x)y=\rho By $ with
$n\times n$ matrices $A,B, q(x)$, where $A,B$ are constant, $B$ is diagonal,
$A$ and $q(x)$ are off-diagonal, $q(\cdot)\in W^1_1[0,\infty)$. Some
distinguished fundamental system of solutions is constructed. Also, we discuss
the inverse scattering problem and obtain the uniqueness result.
