The dynamics of Fermi resonance solitary waves propagating along two p
arallel interfaces in a layered organic semiconductor system is invest
igated both analytically and numerically. It is shown that the interac
tion between solitary waves leads to their attraction or repulsion, de
pending on their initial phase difference. In the case of attraction t
he solitary waves create a bound state, and their centers oscillate in
time with respect to their common mass center. The corresponding peri
od of oscillations is calculated. It is found that the amplitudes and
widths of the solitary waves also oscillate in time.