Abstract
Within general relativity, we construct sequences of rapidly rotating Dirac stars consisting of a spinor fluid described by an effective equation of state. We find the physically relevant domain of stable configurations and calculate their principal characteristics which are completely determined by the central density of the spinor fluid, the mass of the nonlinear spinor field, and the velocity of rotation. It is demonstrated that for a certain choice of the spinor field mass, the main physical characteristics of the Dirac stars are close to those that are typical of rotating neutron stars.