The constant-NPT Monte Carlo method of statistical mechanics has been used to study a monolayer of hard oblate spheroids. The spheroids are free to rotate, but their centres are confined to a plane. Order parameters, configu-rational free energy, and singlet orientation distributions are calculated. It is found that orientational ordering occurs in two steps, as density is increased from zero. First the spheroids' symmetry axes gradually tip into the plane. Then, for sufficiently oblate spheroids, the major axes align in a continuous transition to a state of nematic order. The second orientation ordering shifts to lower density as spheroid eccentricity increases.