  We present evidence for unconventional superconducting fluctuations in a
heavy-fermion compound CeNi$_2$Ge$_2$. The temperature dependence of the
$^{73}$Ge nuclear-spin-lattice-relaxation rate $1/T_1$ indicates the
development of magnetic correlations and the formation of a Fermi-liquid state
at temperatures lower than $T_{\rm FL}=0.4$ K, where $1/T_1T$ is constant. The
resistance and $1/T_1T$ measured on an as-grown sample decrease below $T_{\rm
c}^{\rm onset} = 0.2$ K and $T_{\rm c}^{\rm NQR} = 0.1$ K, respectively; these
are indicative of the onset of superconductivity. However, after annealing the
sample to improve its quality, these superconducting signatures disappear.
These results are consistent with the emergence of unconventional
superconducting fluctuations in close proximity to a quantum critical point
from the superconducting to the normal phase in CeNi$_2$Ge$_2$.
