  The recently reported subgap structures observed in the current-voltage
characteristic of intrinsic Josephson junctions in the high-T_c superconductors
Tl_2Ba_2Ca_2Cu_3O_{10+\delta} and Bi_2Sr_2CaCu_2O_{8+\delta} are explained by
the coupling between c-axis phonons and Josephson oscillations. A model is
developed where c-axis lattice vibrations between adjacent superconducting
multilayers are excited by the Josephson oscillations in a resistive junction.
The voltages of the lowest structures correspond well to the frequencies of
longitudinal c-axis phonons with large oscillator strength in the two
materials, providing a new measurement technique for this quantity.
