A pure radiative method is presented for measuring the directionally-dependent thermal diffusivities of anisotropic solids, especially of free-standing films. A real point and line source are realized by a focussed laser beam. Both configurations allow measurements of the anisotropic thermal diffusivity. Because of the smaller power density applied for the line source, this method is very suited for thermic sensitive films. Virtual image sources are used to account for the boundary conditions of a rectangular slab. The temperature vs time curves are recorded by infrared radiation using an InSb-detector. They are fitted to the solution For a constant heat source switched on at time zero (step heating) disregarding the prefactor. Thus, there is no need to know the absorption coefficient or the absolute temperature rise of the sample. The influence of sample dimensions and of radiative losses is investigated. For sufficiently thin samples a two-dimensional treatment is suited. Extrapolating the diffusivities determined in different time spans to zero heating time excludes radiation losses. A comparison to results from steady-state methods for well-defined samples confirm the reliability of the method. Representative results on highly oriented polymers are presented.