  In the theory of nonlinear partial differential equations we need to explain
superposition operators. For modulation spaces equipped with particular
ultradifferentiable weights this was done in \cite{rrs}. In this paper we
introduce a class of general ultradifferentiable weights for modulation spaces
$\mathcal{M}^{w_*}_{p,q}(\mathbb{R}^n)$ which have at most subexponential
growth. We establish analytic as well as non-analytic superposition results in
the spaces $\mathcal{M}^{w_*}_{p,q}(\mathbb{R}^n)$.
