The possibility of constructing an asymptotic solution of a two-point boundary value problem for a linear singularly perturbed system of differential equations with an identically degenerate matrix at the derivatives is investigated in the case when the limit combination of matrices has a multiple zero eigenvalue, which corresponds to an elementary divisor of the same multiplicity. The conditions for the existence of a unique solution of this boundary value problem are found and its asymptotics are constructed in the form of expansions in fractional powers of a small parameter. The study uses the results of the asymptotic analysis of the general solution of linear singularly perturbed systems of differential equations with degeneracies.

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