  By generalizing the Miura transformation for $\Ww_N$ to other classical $\Ww$
algebras obtained by hamiltonian reduction, we find realisations of these
algebras in terms of relatively simple non-abelian current algebras, e.g.
$\widehat{sl(2)}\times \widehat{u(1)}^N$, generalizing the free field
realisation of $\Ww_N$. As an example, we present the $\widehat{sl(2)}\times
\widehat{u(1)}$ realisation of $\Ww_3^2$, which we also quantize. By a specific
example, we also show how the realisation of $\Ww_N$ with the currents of
$\Ww_{N-1}$ and a free boson can be generalized to certain classes of
``extended'' $\Ww_N$ algebras.
