Solid state interdiffusions between a thin film of erbium deposited under vacuum conditions and (001) and (111) GaAs substrates were investigated in the temperature range 350-800-degrees-C. Complementary analysis methods (RBS, X-ray diffraction) allow us to point out, according to annealing temperatures, successives steps of the interaction corresponding to different mixtures of phases, essentially binaries. These steps are strongly depending on the GaAs substrate orientation, especially the final step of the interdiffusions. On (001) GaAs, only two steps have been observed : no visible interaction is noticed between erbium and GaAs before 600-degrees-C; the interaction begins at 600-degrees-C. evolves slightly and leads at 800-degrees-C to the nominal composition << Er10GaAs >> which corresponds to a mixture of several phases Er5Ga3, Er and ErAs. On (111) GaAs. several steps of interaction have been found ; first of all, erbium reacts with the substrate at 400-degrees-C (Er5Ga, + Er mixture). then the reaction is continuing at 600-degrees-C (Er5Ga3 + Er + ErAs mixture) before reaching at 800-degrees-C the nominal composition << Er1.5GaAs >>, which is in fact a mixture of the three binaries ErAs + ErGa2 + Er3Ga5. It can be noticed that the 800-degrees-C annealing is not sufficient to reach the mixture of the phases ErAs + Ga which, according to the ternary phase diagram, should be the final stage of the interaction Er/GaAs. The analysis of the Er/GaAs interdiffusions shows that ErAs is the << key >> compound around which the interaction progresses. This compound appears as an ideal candidate to realize epitaxial ErAs/GaAs heterostructures.