In this paper we derive a differential-difference equation for a circuit involving a lossless transmission line and we give conditions for global asymptotic stability of an equilibrium point, existence and stability of forced oscillations. Some of such problems have been investigated for an equation obtained by R. K. Brayton [Quart. J. Appl. Math. 24 (1967), 289-301; O. Lopes, SIAM J. Appl. Math., to appear; M. Slemrod, J. Math. Anal. Appl. 36 (1971), 22-40] but, for ours (which governs the same physical problem), better results can be proved. By using suitable Liapunov functionals, we reduce the problem of stability and uniform ultimate boundedness to a scalar ordinary differential inequality. © 1976.553686698The Society of Photo-Optical Instrumentation Engineers (SPIE)Brayton, Nonlinear oscillations in a distributed network (1967) Quart. J. Appl. Math., 24, pp. 289-301Hale, Forward and backward continuation for neutral equations (1971) J. Differential Eqs., 9Hale, Cruz, Existence, uniqueness and continuous dependence for hereditary systems (1970) Ann. di Mat. Pura, 4, p. 85Hale, Cruz, Stability of neutral equations (1970) Journal of Differential Equations, 7Hale, Lopes, Fixed point theorems and dissipatine processes (1973) Journal of Differential Equations, 13O. Lopes, Periodic solutions in neutral equations, SIAM J. Appl. Math., to appearSlemrod, Nonexistence of oscillations in a nonlinear distributed network (1971) J. Math. Anal. Appl., 36, pp. 22-40