Digital fiber-optic networks are the basis of today''s communication infrastructure. The maximum capacity that can be transmitted over a single optical fiber is ultimately limited by the nonlinear properties of the fibre. The parameters of the link design are usually optimised by numeric simulations. Analytic descriptions of the nonlinear perturbation of the received signal can help to reduce the parameter space which has to be simulated. In order to expose the fundamental laws governing the nonlinear perturbation of the received signal, a simple analytic model is derived. A special emphasis of the work lies on the analysis of transmission systems with periodic compensation of the chromatic dispersion. Both amplitude-shift keying signals as well as phase-shift keying signals are considered. The influence of multilevel modulation is discussed in the context of differential quadrature phase-shift keying. Furthermore, universal laws for the impact of nonlinear effects such as cross-phase modulation (XPM), four-wave mixing (FWM) and self-phase modulation (SPM) are presented.