The dielectronic satellite lines from the ls21a 3lb and ls31a 31b, double-excited configurations of lithium-like ions have been studied experimentally and theoretically under dense-plasma conditions. Good agreement between theory and measurements performed in laser-target interactions at 0.53 m wavelength, 1014 W/cm2 laser irradiance show that collisional equilibrium conditions are reached between n − 3 singly and double excited levels at electron densities greater than 1022 cm−3 in Al and Si.