Spin-flip rates in GaAs quantum dots can be quite slow, thus opening up the
possibilities to manipulate spin states in the dots. We present here estim
ations of inelastic spin-flip rates mediated by hyperfine interaction with
nuclei. Under general assumptions the nucleus-mediated rate is proportional
to the phonon relaxation rate for the corresponding non-spin-flip transiti
ons. The rate can be accelerated in the vicinity of a singlet-triplet excit
ed state crossing. The small proportionality coefficient depends inversely
on the number of nuclei in the quantum dot. We compare our results with kno
wn mechanisms of spin-flip in GaAs quantum dots.