Existence of unbounded solutions for small initial functions in the van der Pol equation with delayed feedback Delayed feedback is known as one of useful chaos control methods and there has been much work on the topic. On the other hand, the van der Pol equation is a model of electric circuits and is one of classical and important nonlinear systems. Its dynamics is known to be very simple. For example, it can have an equilibrium and periodic orbit and only one of them can be an attractor. In this thesis we study the van der Pol equation subjected to delayed feedback and show that there exist unbounded solutions for small initial conditions and initial functions. This is in contrast to the original equation in which solutions with small initial conditions go to the equilibrium or periodic orbits. We also give numerical simulation results to demonstrate our theoretical result.