  This paper deals with characterizing the freeness and asymptotic freeness of
free multiple integrals with respect to a free Brownian motion or a free
Poisson process. We obtain three characterizations of freeness, in terms of
contraction operators, covariance conditions, and free Malliavin gradients. We
show how these characterizations can be used in order to obtain limit theorems,
transfer principles, and asymptotic properties of converging sequences.
