  In this paper, we completely characterize nuclear Volterra composition
operators $T^\phi_g : \mathcal H^\infty_\nu \longrightarrow \mathcal
H^\infty_\mu$ and $S^\phi_g : \mathcal H^\infty_\nu \longrightarrow \mathcal
H^\infty_\mu$ acting between weighted type spaces in terms of the symbols $g$
and $\phi$ of $T^\phi_g$ and $S^\phi_g$ and weights $\nu$ and $\mu$, when the
weights $\nu$ and $\mu$ are normal weights in the sense of Shields and
Williams. Moreover, nuclear Volterra composition operators acting between
little weighted type spaces and Bloch spaces of order $\beta$ are also
characterized.
