Integro-differential systems in which the matrix multiplying the derivative of the unknown vector function is identically singular are analyzed. This analysis is based on the special properties of the matrix polynomials associated with the original system. An existence theorem is proved, and a numerical method for finding the solution is proposed and justified.

We consider systems of higher order integro-differential equations in which the matrix multiplying the highest derivative of the unknown vector function is identically singular in the domain where the system is considered. We give criteria for the solvability of such systems and initial value problems for these systems as well as examples illustrating the theoretical results.