The Von-Neumann-Mullins relationship for two-dimensional grain growth is modified for the case of grain boundary faceting. It is shown that the anisotropy of grain boundary energy alone slows down the rate of normal grain growth. For highly mobile facets, however, the acceleration of the growth process is possible, accompanied by development of anisotropic microstructure. It is shown that the mean-field approach to the problem of grain growth in highly anisotropic polycrystal results in parabolic growth law similar to that for isotropic systems, with the facet mobility and maximal torque substituting the grain boundary mobility and grain boundary energy in isotropic systems. (C) 2005 Springer Science + Business Media, Inc.