  We have performed Electron Spin Resonance measurements on single crystals of
the doped spin-Peierls compounds CuGe$_{1-y}$Si$_y$O$_3$ and
Cu$_{1-x}$M$_x$GeO$_3$ with M = Zn, Mg, Ni ($x, y\leq 0.1$). The first part of
our experiments was performed in the paramagnetic and spin-Peierls phases at
9.5, 95 and 190 GHz. All non-magnetic impurities (Si, Zn and Mg) were found to
hardly affect the position and linewidth of the single line resonance, in spite
of the moment formation due to the broken chains. In contrast to Si, Zn and
Mg-doping, the presence of Ni (S = 1) at low concentration induces a
spectacular shift towards high fields of the ESR line (up to 40% for x=0.002),
together with a large broadening. This shift is strictly proportional to the
ratio of Ni to Cu susceptibilities: Hence it is strongly enhanced below the
spin-Peierls transition. We interpret this shift and the broadening as due to
the exchange field induced by the Ni ions onto the strongly exchange coupled Cu
spins. Second, the antiferromagnetic resonance was investigated in Ni-doped
samples. The frequency vs magnetic field relation of the resonance is well
explained by the classical theory with orthorhombic anisotropy, with $g$ values
remarkably reduced, in accordance with the study of the spin-Peierls and
paramagnetic phases. The easy, second-easy, and hard axes are found to be $a$,
$c$, and $b$ axes, respectively. These results, which are dominated by the
single ion anisotropy of Ni$^{2+}$, are discussed in comparison with those in
the Zn- and Si-doped CuGeO$_3$.
