We study two Systems of hard biaxial molecules: hard spheroplatelets and hard ellipsoids, using the liquid-crystalline Version of the smoothed density approximation (SDA). The first system is studied for all elongations of the spheroplatelet c, whereas the second only for c ≤ 7. For both Systems, we locate the line of Landau bicritical points at which a direct transition from the iso- tropic phase to the biaxial phase occurs. We find that the density of the iso- tropic phase at the Landau bicritical point is always higher than that at the isotropic-nematic transition in the limit of uniaxial molecules and the difference ranges from 10 to 30 per Cent. For hard ellipsoids, we obtain a similar scaling behaviour at the Landau bicritical point as for spheroplatelets, i.e. b - c1/2where b denotes the breadth of the ellipsoid. © 1990 Taylor & Francis Group, LLC.