How many correlation lengths for multifractals?

It is shown, here in the context of percolation, that one can have multifractal behavior and at the same time a single correlation length. This length sets the scale below which non-trivial scaling behavior occurs and it is controlled by a few relevant operators, as in ordinary critical phenomena. All other correlation lengths may be obtained from simple metric factors. The quantities which lead to an infinite set of exponents are described by a second renormalization group which is slaved to the first one which determines the correlation length. The results are relevant also to the problem of noise in percolating systems.