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We investigate the stability of a biaxial phase in a mixture of rod- and platelike hard ellipsoids with respect to phase separation in two nematic phases. The phase separation was studied by means of Gibbs Ensemble Monte Carlo simulations. We found that a plate-rich nematic was in coexistence with a biaxial ordered phase, instead of the expected rod-rich nematic. The asymmetry in the phase diagram is probably due to the difference in the third and higher virial coefficients of the rods compared to the plates.