A perfectly conducting, nonviscous fluid is assumed to be permeated by an inhomogeneous, time independent magnetic field satisfying the magnetohydrostatic equation. This fluid shall be perturbed by hydromagnetic waves of small amplitude. The wave equation is expressed in a completely covariant form. This formulation allows to search for simplifying coordinate systems intrinsically adapted to the undisturbed field configuration. Hydromagnetic waves with the velocity vector satisfying the equation div v=0, which are the natural generalization of ALFVÉN waves have been investigated especially. It is shown that there are simplifying coordinate systems for the hydromagnetic wave equation. Especially it is shown that the solution of the ALFVÉN wave equation can always be reduced to the solution of an ordinary differential equation if in the equilibrium configuration the current is either perpendicular on the magnetic field line or zero.