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A nonclassical skew-selfadjoint system of two linear differential equations is considered, which depends rationally on the spectral parameter. Systems of this type are related to the sine-Gordon equation. We introduce the notion of W p -functions (Weyl functions) which are defined in a neighborhood of the poles. The main results are theorems on the existence and uniqueness of the Weyl functions, on the uniqueness of the solutions of the inverse problem, and on explicit solutions for the directdoi:10.1215/s0012-7094-01-10931-9 fatcat:llz65wedxvdgxoqjsvya2cgpom