  The nature of the magnetic transition of the half-filled triangular
antiferromagnet Ag$_{2}$NiO$_2$ with $T_{\rm N}$=56K was studied with positive
muon-spin-rotation and relaxation ($\mu^+$SR) spectroscopy. Zero field
$\mu^+$SR measurements indicate the existence of a static internal magnetic
field at temperatures below $T_{\rm N}$. Two components with slightly different
precession frequencies and wide internal-field distributions suggest the
formation of an incommensurate antiferromagnetic order below 56 K. This implies
that the antifrerromagnetic interaction is predominant in the NiO$_2$ plane in
contrast to the case of the related compound NaNiO$_2$. An additional
transition was found at $\sim$22 K by both $\mu^+$SR and susceptibility
measurements. It was also clarified that the transition at $\sim$260 K observed
in the susceptibility of Ag$_{2}$NiO$_{2}$ is induced by a purely structural
transition.
