**ABSTRACT:**

We discuss algebraic properties of the Weyl product acting on modulation spaces. For a certain class of weight functions w we prove that M_w^{p,q} is an algebra under the Weyl product if p \in [1,\infty] and 1 \leq q \leq \min(p,p'). For the remaining cases p \in [1,\infty] and \min(p,p') < q \leq \infty we show that the unweighted spaces M^{p,q} are not algebras under the Weyl product. The work has been done jointly with A. Holst and J. Toft.