Abstract: We study a nonstationary Maxwell system in (Formula presented.) with dielectric permittivity (Formula presented.) and magnetic permeability μ. Here (Formula presented.) is a positive definite bounded symmetric (Formula presented.)-matrix- valued function periodic with respect to some lattice and μ is a constant positive (Formula presented.) matrix. We obtain approximations for the solutions in the (Formula presented.)-norm for a fixed time with error estimates of operator type.