A system for general classification of non-uniform transmission lines—by transforming the independent variablex(representing distance) of the telegraphists' second-order linear differential equation to another independent variablew=F(x)which is some function ofxand then by constraining the transformed telegraphists' equation to simulate a standard second-order linear differential equation (the solution of which is wellknown) expressed in terms of the same independent variable,w—is introduced. On the basis of this classification, two sets of generalized expressions for non-uniformity corresponding to each of the classes of the non-uniform lines have been derived. One set is in terms of the new independent variablewwhich may be any arbitrary function ofxand the other set is in terms of another arbitrary functionf(x)[org(x)] ofxwheref(x)[org(x)] characterizes the series impedanceZ(x)[or shunt admittanceY(x)] per unit length of the line in the formZ(x) = Zof(x)[orY(x) = Yog(x)] withZo[orYo] being a constant of impedance [or admittance]. Corresponding to each set of generalized pattern of non-uniformity, one general solution for voltage for each class of line has been worked out. It is shown that the two sets of non-uniformity, derived for each class, are the most general ones and they require no further generalization.3 Most of the non-uniform transmission lines, for which solutions are hitherto available, are found to be the members of the general classes introduced here. In addition, the generalized patterns of non-uniformity of certain new classes of non-uniform lines are derived and the applicability of this basic principle of classification for obtaining a number of transformable sub-classes is illustrated.