  We generalize the KPZ equation to an O(3) $N=2j+1$ component model. In the
limit $N \to \infty$ we show that the mode coupling equations become exact.
Solving these approximately we find that the dynamic exponent $z$ increases
from $3/2$ for $d=1$ to $2$ at the dimension $d\approx3.6$. For $d=1$ it can be
shown analytically that $z=3/2$ for all $j$. The case $j=2$ for $d=2$ is
investigated by numerical integration of the KPZ equation.
