A nonlinear evolution system of hydrodynamic-type equations describing a three-dimensional multisublattice magnet is studied. An explicit expression is obtained for the energy density function of magnetic systems whose energy density is invariant to right- and left-spin rotations. Exact solutions for spin density are obtained in the form of helical waves for quadratic–biquadratic dependence of the energy density (in terms of Cartan’s invariant functions) in three-dimensional case. Solutions are also obtained for magnon fields inducing such waves. The existence of backward helical waves is predicted. ©1998 American Institute of Physics.