Considering the theme, this chapter is a continuation of Chapter 11. The physics of the ordinary (parametrical) FELs is studied, yet, as one can see, the given material below is essentially different from that of the previous chapter. Contrary to Chapter 11, where the weak-signal theory is the main object of attention, in the present chapter, we will concentrate on the cubic-nonlinear theory of the Dopplertrons and H-Ubitrons. This includes the study of the effect of the saturation of the ampli£cation of the electromagnetic signal as the key physical mechanism for the nonlinear theory of any electronic device with long-time interaction. In addition to this, we describe a peculiar hierarchic calculation technology as well as the methodology of the nonlinear analysis of such kind, both of which deserve attention.