  We report on a zero-field 63Cu nuclear quadrupole resonance (NQR) study of
nonmagnetic Mg impurity substituted Cu1-xMgxGeO3 (single crystals; the
spin-Peierls transition temperature Tsp~14, 13.5, and 11 K for x=0, 0.0043, and
0.020) in a temperature range from 4.2 K to 250 K. We found that below T*~77 K,
Cu NQR spectra are broadened and nonexponential Cu nuclear spin-lattice
relaxation increases for undoped and more remarkably for Mg-doped samples. The
results indicate that random lattice distortion and impurity-induced spins
appear below T*, which we associate with a precursor of the spin-Peierls
transition. Conventional magnetic critical slowing down does not appear down to
4.2 K below Tsp.
