DEVELOPMENT OF THE METHOD OF CHARACTERISTICS FOR A SYSTEM OF MAXWELL ELECTRODYNAMIC EQUATIONSS. M. Bosyakov and M. D. Martynenko UDC 539.3 Expressions for the velocities of propagation of the discontinuity surfaces in a homogeneous anisotropic medium have been obtained and equations of bicharacteristics have been derived. Using them, the surfaces of inverse velocities and three-dimensional wave fronts of electromagnetic waves have been constructed for different values of the permittivities and their features have been investigated. Belarusian State University, Minsk, Belarus. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 76, No. 2, pp. 138-144, March-April, 2003. Original article submitted October 17, 2002.