A bonded interface between two solids which have an appropriate mismatch in their mechanical properties can support Stoneley waves. The question investigated is whether an unbonded interface, which is unable to transmit tensile tractions, can sustain interface waves that involve localized separation. The answer is affirmative, and the following conclusions are reached: 1. The solids must be pressed together. 2. All combinations of materials can sustain interface waves involving separation. 3. The phase velocity of the interface waves is not fixed but lies within a range of values. For instance, in case of identical materials, the phase velocity may have any value falling between the velocities of Rayleigh and transverse waves (cR < c < cT). 4. The interface waves do not involve a free amplitude, and the wave form is fixed. However, the length of the separation zones remains arbitrary, so that energy can still be transmitted at greatly different rates. 5. The solids move apart in the sense of an average displacement. 6. The gaps are symmetric about the centers of the separation zones, and the interface tractions are symmetric about the centers of the contact zones. 7. The interface waves involving separation exhibit features that are similar to those encountered in dynamic fracture. The interface tractions are square-root singular at both leading and trailing ends of the gaps. The two solids pull apart at the leading ends of the gaps with infinite discontinuities in particle velocities. The solids slam together at the trailing ends with exactly the opposite velocity discontinuities.