This chapter considers continuous differential equation growth models with a time delay in the productive operation of installed capital. By a local nonlinear analysis, it is demonstrated that the equilibrium becomes unstable in a Hopf bifurcation for sufficiently large delays. Periodic solutions in the form of limit cycles are created in the bifurcation. In a specific example with a CD production function we show the bifurcation is supercritical such that the limit cycles are stable and exist for delays larger than the critical value. By numerical simulations with a CES production function, we show that the model may exhibit “square wave” solutions and “chaos” (aperiodic oscillations) for our single delay differential equation, if the delay is very large. The model phase portrait integrates the phenomena of economic growth and cycles.