Two flat isotropic elastic half-spaces, of different material properties, are pressed together and slide against each other with a constant coefficient of friction. Although a nominally steady-state solution exists, an analysis of the dynamic problem demonstrates that the steady solution can be dynamically unstable. Eigenvalues with positive real parts give rise to self-excited motion which occurs for a wide range of material pairs, coefficients of friction, and sliding velocities (including very low speeds). These self-excited oscillations are generally confined to the region near the interface and can lead either to regions of loss of contact or to areas of stick slip. The mechanism responsible for the instability is essentially one of destabilization of interfacial (slip) waves. It is expected that these vibrations might play an important role in the behavior of sliding members with dry friction.