The chain parameters of five well known regular nonuniform transmission lines (n.u.t.l.s) are evaluated. In these evaluations, the differential interrelations among the chain parameters of the n.u.t.l.s. in the form of 2nd-order matrix differential equations with their boundary conditions are employed. The method used is applicable to any nonuniformity, provided that the 2nd-order differential equations formed by the chain parameters have regular singularities.