Abstract: We study the asymptotic distribution of discrete eigenvalues near the bottom of the essential spectrum for two dimensional Pauli operator with magnetic field perturbed by electric fields falling off at infinity. Unperturbed Pauli operator has the zero energy as an isolated eigenvaue with infinite multiplicity if the magnetic field is bounded from below by some positive constant. We first study the asymptotic distribution of discrete eigenvalues around the zero eigenvalue in this case. We consider also the case of the magnetic field which converges to 0 at infinity.