Exact traveling-wave solutions of the time-dependent Landau-Ginzburg equation for a system undergoing first-order phase transition are found. These are two general types of solutions : domain walls which interpolate between two minima in the potential and relaxation modes which interpolate between a minimum and a maximum in the potential. The solutions are found in the presence of an external field. An estimation of the parameters of the solutions for N-[p-methoxybenzylidine]-p-butylaniline (MBBA) is performed.