The paper is devoted to so-called secondary turning point problems. Therefore, WKB solutions to \(n\)th-order differential equations are introduced that can be regarded as generalization of the classical WKB solutions to the one-dimensional Schrödinger equation. Maximal existence regions of the true solutions, whose asymptotic expansions are WKB solutions to the stretched equation, are constructed. Finally, existence theorems of the solutions to the reduced differential equations are proved, and a matching matrix is computed.