  In this contribution, we study the orthogonality conditions satisfied by
Al-Salam-Carlitz polynomials $U^{(a)}_n(x;q)$ when the parameters $a$ and $q$
are not necessarily real nor `classical', i.e., the linear functional $\bf u$
with respect to such polynomial sequence is quasi-definite and not positive
definite. We establish orthogonality on a simple contour in the complex plane
which depends on the parameters. In all cases we show that the orthogonality
conditions characterize the Al-Salam-Carlitz polynomials $U_n^{(a)}(x;q)$ of
degree $n$ up to a constant factor. We also obtain a generalization of the
unique generating function for these polynomials.
