•Under investigation is a higher-order nonlinear Schrodinger system for the simultaneous propagation of two ultrashort optical pulses in an optical fiber.•With respect to the two-component electric fields, infinitely-many conservation laws and N-fold binary Darboux transformation are derived via the symbolic computation.•Nondegenerate one dark–dark soliton which is black or gray in each component is obtained. epsilon has no relation with the soliton amplitudes in each component, but has a linear correlation with the soliton velocities.•Overtaking and head-on interactions between the two dark–dark solitons as well as the bound state are depicted. With the decreasing value of sigma_1, the gray solitons’ amplitudes increase, but the black solitons’ amplitudes decrease. With the decreasing value of sigma_2, the gray solitons’ amplitudes increase, but the black solitons’ amplitudes do not change.•Interaction among the three overtaking solitons and interaction between a bound state and one soliton are displayed. We find that the interactions between the two solitons and among the three solitons are elastic. Optical fiber communication system is one of the core supporting systems of the modern internet age. In this paper, under investigation is a higher-order nonlinear Schrödinger system for the simultaneous propagation of two ultrashort optical pulses in an optical fiber. Based on the Lax pair, with respect to the two-component electric fields, infinitely-many conservation laws and one/N-fold binary Darboux transformations are derived, where N=2,3,…. Solitons are discussed: (1) Nondegenerate one dark–dark soliton, which is black or gray in each component, is obtained. ϵ has no relation with the soliton amplitude in each component, but has a linear correlation with the soliton velocities, where ϵ, σ1 and σ2 are the constant coefficients in the system; (2) Overtaking and head-on interactions between the two dark–dark solitons as well as the bound state are depicted. With the decreasing value of σ1, the gray solitons’ amplitudes increase, but the black solitons’ amplitudes decrease. With the decreasing value of σ2, the gray solitons’ amplitudes increase, but the black solitons’ amplitudes do not change; (3) Interaction among the three overtaking solitons and interaction between a bound state and one soliton are displayed. We find that the interactions between the two solitons and among the three solitons are elastic.