  The magnetic properties of Li_{1-x}Ni_{1+x}O_2 compounds with x ranging
between 0.02 and 0.2 are investigated. Magnetization and ac susceptibility
measured at temperatures between 2 K and 300 K reveal a high sensitivity to x,
the excess Nickel concentration. We introduce a percolation model describing
the formation of Ni clusters and use an Ising model to simulate their magnetic
properties. Numerical results, obtained by a Monte-Carlo technique, are
compared to the experimental data. We show the existence of a critical
concentration, x_c = 0.136, locating the Ni percolation threshold. The system
is superparamagnetic for x<x_c, while it is ferrimagnetic for x>x_c. The 180
Ni-O-Ni inter-plane super-exchange coupling J_\perp \simeq -110K is confirmed
to be the predominant magnetic interaction. From the low temperature behavior,
we find a clear indication of a 90 Ni-O-Ni intra-plane antiferromagnetic
interaction $J_\parallel \simeq -1.5K$ which implies magnetic frustration.
