In this paper, the solution of higher order linear homogeneous complex σ-α descriptor matrix differential systems of Apostol-Kolodner type is investigated by considering pairs of complex matrices with symmetric and skew symmetric structural properties. The results are very general, and they derive under congruence of the Thompson canonical form. The regularity (or singularity) of a matrix pencil pre-determines the number of sub-systems respectively. The special structure of these kinds of systems derives from applications in engineering, physical sciences and economics. A numerical example illustrates the main findings of the paper.