  In this paper we consider nodal radial solutions $u_\epsilon$ to the problem
\[ \begin{cases} -\Delta u=\lambda ue^{u^2+|u|^{1+\epsilon}}&\text{ in }B,\\
u=0&\text{ on }\partial B. \end{cases} \] and we study their asymptotic
behaviour as $\epsilon\searrow0$, $\epsilon>0$. We show that when $u_\epsilon$
has $k$ interior zeros, it exhibits a multiple blow-up behaviour in the first
$k$ nodal sets while it converges to the least energy solution of the problem
with $\epsilon=0$ in the $(k+1)$-th one. We also prove that in each
concentration set, with an appropriate scaling, $u_\epsilon$ converges to the
solution of the classical Liouville problem in $R^2$.
