We study the connectivity propel-ties of the complementary set in Poisson m
ultiscale percolation model and in Mandelbrot's percolation model in arbitr
ary dimension. By using a result about majorizing dependent random fields b
y Bernoulli fields, we prove that if the selection parameter is less than c
ertain critical value, then, by choosing the scaling parameter large enough
, we can assure that there is no percolation in the complementary set.