<p>The article considers a boundary value problem for a degenerate equation of high even order involving a third-order derivative. The solution to the problem is constructed as a series in eigenfunctions of the spectral problem for a degenerate ordinary differential equation of high even order with lower terms. Sufficient conditions for expansion in terms of the system of eigenfunctions of the spectral problem under study are found. In this case, the boundary value problem for a one-dimensional differential equation of the third order with lower terms is also solved explicitly. A criterion for the unique solvability of the solution to the problem is obtained.</p>