We study the electronic and magnetic properties of T2AlC (T = Ti and Cr) compounds in the density-functional theory using the generalized gradient approximation (GGA) with consideration of strong Coulomb correlations (GGA+U) in the framework of the fully relativistic spin-polarized Dirac linear muffin-tin orbital (LMTO) band-structure method. The X-ray absorption spectra and X-ray magnetic circular dichroism (XMCD) at the Cr L2,3 and Cr, Ti, and C K edges were investigated theoretically. The calculated results are in good agreement with experimental data. The effect of the electric quadrupole E2 and magnetic dipole M1 transitions at the Cr K edge has been investigated.