  We investigate generalizations of the Cram\'er theorem. This theorem asserts
that a Gaussian random variable can be decomposed into the sum of independent
random variables if and only if they are Gaussian. We prove asymptotic
counterparts of such decomposition results for multiple Wiener integrals and
prove that similar results are true for the (asymptotic) decomposition of the
semicircular distribution into free multiple Wigner integrals.
