In this paper, we consider some nonlinear phenomena such as "self-oscillation," "synchronization," and "asynchronous quenching" in a distributed system. The system consists of a lossless transmission line terminated with a tunnel diode and a lumped parallel capacitance on one end. Such a system is governed by a partial differential equation (wave equation) and nonlinear boundary conditions. By introducing the d'Alembert solution of the wave equation, the equation describing the system is reduced to a nonlinear differential-difference equation. We have made a theoretical analysis of the above system following a nonlinear technique and obtained some interesting results. Also, we present examples of waveforms of self-oscillation obtained by computation and experiment, and show some experimental results which are in good agreement with the theoretical results.