We study the interaction of small amplitude, long-wavelength solitary waves in the Fermi–Pasta–Ulam model with general nearest-neighbour interaction potential. We establish global-in-time existence and stability of counter-propagating solitary wave solutions. These solutions are close to the linear superposition of two solitary waves for large positive and negative values of time; for intermediate values of time these solutions describe the interaction of two counter-propagating pulses. These solutions are stable with respect to perturbations in ℓ2 and asymptotically stable with respect to perturbations which decay exponentially at spatial ±∞.