  We present results of numerical simulations of kinetic roughening for a
growth model with surface diffusion (the Wolf-Villain model) in 3+1 and
4+1~dimensions using lattices of a linear size up to $L=64$ in 3+1~D and $L=32$
in 4+1~D. The effective exponents calculated both from the surface width and
from the height--height correlation function are much larger than those
expected based on results in lower dimensions, due to a growth instability
which leads to the evolution of large mounded structures on the surface. An
increase of the range for incorporation of a freshly deposited particle leads
to a decrease of the roughness but does not suppress the instability.
