Linear waves superimposed on an arbitrary basic state in ideal magnetohydrodynamics (MHD) are studied by an asymptotic expansion valid for short wavelengths. It has not been necessary to introduce any assumption beyond the usual regularity assumptions on the arbitrarily given solution which represents the basic state in this paper; it may even be time dependent. The theory also allows for a gravitational potential; it may therefore be applied both in astrophysics and in problems related to thermonuclear fusion. The linearized equations for the perturbations of the basic state are found in the form of a symmetric hyperbolic system. This symmetric hyperbolic system is shown to possess characteristics of nonuniform multiplicity, which implies that waves of different types may interact. In particular, it is shown that mass, Alfve´n, and slow magnetoacoustic waves will persistently interact in the exceptional case where the local wavenumber vector is perpendicular to the magnetic field. The equations describing this interaction are found in the form of a weakly coupled hyperbolic system. This weakly coupled hyperbolic system is studied in a number of special cases and detailed analytic results are obtained for some such cases. The results show that the interaction of the waves may be one of the major causes of instability of the basic state. It seems beyond doubt that the interacting waves contain the physically relevant parts of the waves, which often are referred to as ballooning modes, including Suydam and Mercier modes.