The excitation of travelling nonlinear Langmuir waves in a plasma by a relativistic electron bunch is considered. The nonlinear excitation is described as relativistic oscillations of the momentum of plasma electrons in effective potentials produced by the bunch and by the perturbation of the electron density of the plasma. The condition for the optimal excitation of the wave yields a relation between the density of the plasma, the density of the bunch and the length of the bunch. Numerical results support the theoretical analysis and demonstrate a deep nonlinear modulation of the electron plasma density and excitation of a large-amplitude longitudinal field at realistic plasma and electron pulse parameters. The back action of the wave field on the bunch is considered. It is shown that sharp peaks develop in its density distribution.