The nonlinear evolution of perturbations in a magnetized plasma subject to the radiation-driven thermal instability (RDTI) is investigated analytically in a simplified model. The perturbed plasma motions are assumed to be one-dimensional and perpendicular to the magnetic field. The intermediate- and long-wavelength limits of the RDTI are considered. In the former limit, the force balance sets in rapidly, on the magneto-acoustic time scale and we assume the total (thermal-magnetic) pressure remains constant. By transforming to Lagrangian variables, the problem is reduced to a single generalized reaction-diffusion equation, which is employed to analyze the two following stages of the RDTI. The first develops on the radiative time scale, when the heat conduction is insignificant, while the second usually occurs on a much longer, heat conduction-related time scale. For the first stage, a simple analytical solution is found, which describes the development of a strong plasma stratification (coexisting hot rarefied phase and cool dense phase) across the magnetic field. Slow erosion of the stratification in the form of almost uniform motion, collision and “annihilation” of the inter-phase boundaries generally occurs at the second stage.