  We study percolation as a critical phenomenon on a multifractal support. The
scaling exponents of the the infinite cluster size ($\beta$ exponent) and the
fractal dimension of the percolation cluster ($d_f$) are quantities that seem
do not depend on local anisotropies. These two quantities have the same value
as in the standard percolation in regular bidimensional lattices. On the other
side, the scaling of the correlation length ($\nu$ exponent) unfolds new
universality classes due to the local anisotropy of the critical percolation
cluster. We use two critical exponents $\nu$ according to the percolation
criterion for crossing the lattice in either direction or in both directions.
Moreover $\nu$ is related to a parameter that characterizes the stretching of
the blocks forming the tilling of the multifractal.
