  We prove a Beurling-Helson type theorem on modulation spaces. More precisely,
we show that the only $\mathcal{C}^{1}$ changes of variables that leave
invariant the modulation spaces $\M{p,q}(\rd)$ are affine functions on $\rd$. A
special case of our result involving the Sj\"ostrand algebra was considered
earlier by A. Boulkhemair.
