  A series of high-quality single crystals of Cu$_{1-x}$Zn$_x$GeO$_3$ have been
examined by neutron scattering techniques. An antiferromagnetic (AF) ordering
is confirmed for samples with $x\geq 0.02$, in complete agreement with previous
reports. We show that the spin-Peierls (SP) phase transition persists to 6\%
Zn, whereas previous magnetic susceptibility measurements reported a
deterioration of the SP transition above 2\% Zn. We present some details of the
successive transitions upon lowering temperature into the spin-Peierls phase
which is followed by a transition into an antiferromagnetically ordered phase.
Below the N\'eel temperature we observe the coexistence of the SP lattice
dimerization and AF states.
