In this paper, we study the modulational instability (MI) in a biexciton molecular chain taking into account the saturable nonlinearity effects (SNE). Under the adiabatic approximation, the biexciton system is reduced to two coupled nonlinear Schrödinger equations. We perform the linear stability analysis of continuous wave solutions of the coupled system. This analysis reveals that the MI gain is deeply influenced by the SNE. Indeed, the gain spectrum decreases when increasing the saturable nonlinearity parameters. The numerical simulations reveal that the system exhibits incoherent periodic array of patterns and we also observe train of pulses due to the SNE.
