  We discuss when the nonlinear operation $f\mapsto F(f)$ maps the modulation
space $M^{p,q}_s(\mathbb{R}^n)$ ($1 \leq p,q \leq \infty$) to the same space
again. It is known that $M^{p,q}_s(\mathbb{R}^n)$ is a multiplication algebra
when $s > n-n/q$, hence it is true for this space if $F$ is entire. We claim
that it is still true for non-analytic $F$ when $q\geq4/3$.
