The absorption due to H2–H2 complexes is investigated theoretically. The potential and dipole surfaces for the complex are taken from the literature. Quantum dynamical calculations of the roto-translational absorption spectrum are performed. Special attention is paid to the fine features due to hydrogen dimers, (H2)2, at the centers of the collision-induced rotational S(0) and S(1) transitions. The computed absorption coefficients are used to analyze the spectra of the four giant planets of our solar system.