The semirelativistic hydrodynamic equations of motion of de Groot and Mazur [Non-Equilibrium Thermodynamics (North-Holland, Amsterdam, 1962)] for a fluid with polarization and magnetization are derived from the relativistic energy-momentum conservation equation, mass conservation, and Maxwell's equations on the basis of a systematic expansion in inverse powers of the velocity of light. A modification of the de Groot-Suttorp field energy-momentum tensor [de Groot and Suttorp, Foundations of Electrodynamics (North-Holland, Amsterdam, 1972)] based on a shift of terms to the internal energy density of the fluid yields relatively simple expressions for energy density, energy current density, momentum density, and stress tensor. (C) 2004 American Institute of Physics.