2-Coverings of classical groups

In this paper we show that if $n\ge 5$ and $G$ is any of the groups $S{U}_n(q)$ with $n\mathrm{\ne }6,$ $S{p}_{2n}(q)$ with $q$ odd, ${\mathrm{\Omega }}_{2n+1}(q),$ ${\mathrm{\Omega }}_{2n}^{\pm }(q),$ then $G$ and the simple group $\text{barG}=G\mathrm{/}Z(G)$ are not 2-coverable. Moreover the only 2-covering of $S{p}_{2n}(q),$ with $q$ even, has components $O_{2n}^{-}(q)$ and $O_{2n}^{+}(q)\mathrm{.}$