  In this paper, we introduce and study the notion of strongly $\phi$-$w$-flat
modules. The $\phi$-$w$-weak global dimension $\phi$-$w$-w.gl.dim$(R)$ of an
NP-ring $R$ is also introduced and studied. We characterize $\phi$-\Prufer\
$v$-multiplication strongly $\phi$-rings in terms of strongly $\phi$-$w$-flat
modules.
