We consider a fluid of hard boomerangs, each composed of two hard spherocylinders joined at their ends at an angle Y. The resulting particle is nonconvex and biaxial. The occurence of nematic order in such a system has been investigated using Straley’s theory, which is a simplificaton of Onsager’s second-virial treatment of long hard rods, and by bifurcation analysis. The excluded volume of two hard boomerangs has been approximated by the sum of excluded volumes of pairs of constituent spherocylinders, and the angle-dependent second-virial coefficient has been replaced by a low-order interpolating function. At the so-called Landau point, YLandau » 107.4°, the fluid undergoes a continuous transition from the isotropic to a biaxial nematic (B) phase. For Y ¹ YLandau ordering is via a first-order transition into a rod-like uniaxial neamtic phase (N+) if Y > YLandau, or a plate-like uniaxial nematic (N­) phase if Y < YLandau. The B phase is separated from the N+ and N­ phases by two lines of continuous transitions meeting at the Landau point. This topology of the phase diagram is in agreement with previous studies of spheroplatelets and biaxial ellipsoids. We have checked the accuracy of our theory by performing numerical calculations of the angle-dependent second virial coefficient, which yields YLandau » 110° for very long rods, and YLandau » 90° for short rods. In the latter case, the I–N transitions occur at unphysically high packing fractions, reflecting the inappropriateness of the second-virial approximation in this limit.