  We provide a characterisation of $(n-1)$-spreads in $\mathrm{PG}(rn-1,q)$
that have $r$ normal elements in general position. In the same way, we obtain a
geometric characterisation of Desarguesian $(n-1)$-spreads in
$\mathrm{PG}(rn-1,q)$, $r>2$.
