In order to interpret the phonon-assisted optical transitions in semic
onductor quantum dots, a theory is developed comprising the exciton in
teraction with both adiabatic and Jahn-Teller phonons and also the ext
ernal nonadiabaticity (pseudo-Jahn-Teller effect). The effects of nona
diabaticity of the exciton-phonon system are shown to lead to a signif
icant enhancement of phonon-assisted transition probabilities and to m
ultiphonon optical spectra that are considerably different from the Fr
anck-Condon progression. The calculated relative intensity of the phon
on satellites and its temperature dependence compare well with the exp
erimental data on the photoluminescence of CdSe quantum dots, both col
loidal and embedded in glass.