[en] The evolution of spatially periodic unstable solutions to the Ginzburg-Landau equation is considered. These solutions are shown to remain pointwise bound (Lagrange stable). The first step in the route to chaos is limit-cycle behavior. This is treated by perturbation theory and results in a factorable form. Agreement between the perturbation result and an exact numerical integration is shown to be excellent. These limit cycle solutions are related in a very natural way to well known spatially and temporally periodic solutions to the cubic Schroedinger equation. The secondary instability curve in parameter space is constructed marking the transition from limit cycle to two torus motion. This is done approximately using perturbation theory, and exactly using Floquet theory. A system of 3 ordinary differential equations in space is derived governing the stable limit cycle solutions. Special properties of this system are examined, equilibrium solutions are discussed, and a more general problem associated with this system is mentioned