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It was discovered by Brayton [1, 2], in connection with the study of transmission lines, that certain mixed initial-boundary problems can be reduced to initial value problems for associated differential-difference equations. and Krumme [3] obtained a systematic method for effecting this reduction, based on the method of characteristics, and generalized the class of mixed problems under consideration. In this note we shall summarize recent results [4] on these mixed problems, particularly theorems on non-local existence, uniqueness, and continuous dependence of solutions. Applications to transmission line problems will be indicated.