In this study, we are concerned with spectral problems of second-order vector
dynamic equations with two-point boundary value conditions and mixed
derivatives, where the matrix-valued coefficient of the leading term may be
singular, and the domain is non-uniform but finite. A concept of
self-adjointness of the boundary conditions is introduced. The self-adjointness
of the corresponding dynamic operator is discussed on a suitable admissible
function space, and fundamental spectral results are obtained. The dual
orthogonality of eigenfunctions is shown in a special case.