We stufy inhomogeneous transmission lines for which the product of the series impedance and the shunt admittance is a constant. In these devices, we can show that the dynamics of the voltage and current is described by a supersymmetric Hamiltonian. The formalism is then applied to a particular class of inhomogenous lines which admit exact and compact solutions. Our models exhibit different propagation regimes tuned by the strength of the inhomogeneity. © 1986.