  We investigate Laha-Lukacs properties of noncommutative random variables
(processes). We prove that some families of free Meixner distributions can be
characterized by the conditional moments of polynomial functions of degree 3.
We also show that this fact has consequences in describing some free Levy
processes. The proof relies on a combinatorial identity. At the end of this
paper we show that this result can be extended to a q-Gausian variable.
