The presence of accompanying resonances to the longitudinal optical phonon satellites in the optical spectra of semiconductor quantum dots is confirmed theoretically by a non-adiabatic approach of the optical absorption. The theory is applied to simulate features of the optical spectra of small spherical GaAs/AlAs quantum dots. The intensity and the spectral position of the accompanying resonances are influenced by both optically active and dark levels and increase to measurable values with temperature. (c) 2005 Elsevier B.V. All rights reserved.