  We show that the pseudoeffective cone of divisors
$\overline{\text{Eff}}^1(\overline{\mathcal{M}}_{g,n})$ for $g\geq 2$ and
$n\geq 2$ is not polyhedral by showing that the class of the fibre of the
morphism forgetting one point forms an extremal ray of the dual nef cone of
curves $\overline{\text{Nef}}_1(\overline{\mathcal{M}}_{g,n})$ and the cone at
this ray is not polyhedral.
