Spin transitions of cobalt ions in LaCoO3 single crystals have been studied by the method of X-ray magnetic circular dichroism (XMCD) at the K- and L2,3-edges of Co3+ ions. The orbital momentum of cobalt ions obtained for the K-edge at the 3d level in the region of the spin transition in the temperature range from 25 to 120 K increases by a factor of approximately 1.6, whereas the slope of the magnetization curve value in the same temperature range and magnetic field increases by a factor of more than 10. XMCD experiments at the cobalt L2,3-edges demonstrate gradual growth of the ratio of the orbital momentum to the spin one L/S from 0.48 to 0.53 in the temperature range from 60 K to 120 K
