<p>The process of generating galvanic currents by an alternating magnetic field in antiferromagnetic metals and semimetals has been studied on the example of Mn₂Au and CuMnAs. It has been shown that in metallic antiferromagnets of tetragonal symmetry, the external magnetic field leads to the redistribution of the charge density, and, as a result, to the appearance of the electric polarization and bias currents. To calculate magnetogalvanic effects in these materials, a model based on the group theoretical analysis and the Lagrangian formalism has been proposed. The electrical response of the system to the alternating magnetic field varying in time according to the linear and harmonic laws has been calculated. It has been shown that an adiabatically changing external magnetic field generates an electric current, which disappears in saturation fields, and an alternating electric current with a nonzero average value arises with the harmonic modulation of the field.</p>