MPEJ Volume 5, No.2, 22pp Received: Oct 19, 1998, Accepted: Apr 8, 1999 G.D. Raikov Eigenvalue Asymptotics for the Dirac Operator in Strong Constant Magnetic Fields ABSTRACT: We consider the three-dimensional Dirac operator $H$ with constant magnetic field and electric potential which decays at infinity. We study the asymptotic behaviour of the discrete spectrum of $H$ as the norm of the magnetic field grows unboundedly.