The resistive boundary layer theory based on a non-constant-φ asymptotic matching method is reviewed. This theory describes resistive-kink modes, double-tearing modes and forced reconnection. An intrinsic difficulty in this theory is presented. The difficulty is the appearance of an unstable solution for the equilibrium which is stable against tearing modes, i.e.Δ'<0. The origin of the difficulty is clarified. It is an open problem to formulate a boundary layer theory which intrinsically excludes this unstable solution.