The change of the spectra.1 properties of the single-particle Green's
function due to a coupling to optical phonons is investigated for stro
ngly correlated electrons. Except at the bottom of the band the quasip
article pole is considerably broadened due to phonon-induced decay pro
cesses, and phonon-satellite structures appear. The overall coherent b
andwidth is, however, not significantly changed. The phonon induced ma
ss renormalization of a single carrier which propagates in the t-J mod
el on scale J is found to be much larger than in the corresponding unc
orrelated model, except in the limit of J --> 0.