S. Vugalter Bounds States of Atoms in a Homogenneous Magnetic Field (49K, Latex 2e) ABSTRACT. We consider Schr\"odinger operators of atoms in a homogeneous magnetic field. We prove that for each fixed value of the pseudomomentum, the corresponding operator has an infinite number of eigenvalues. The asymptotic of the counting function is studied for values of spectral parameter near the bottom of the essential spectrum.