  In this paper, we introduced $\alpha$-Hurewicz $\&$ $\theta$-Hurewicz
properties in a topological space $X$ and investigated their relationship with
other selective covering properties. We have shown that for an extremally
disconnected semi-regular spaces, the properties: Hurewicz, semi-Hurewicz,
$\alpha$-Hurewicz, $\theta$-Hurewicz, almost-Hurewicz, nearly Hurewicz and
midly Hurewicz are equivalent. We have also proved that for an extremally
disconnected space X, every finite power of X has $\theta$-Hurewicz property if
and only if X has the selection principle $U_{fin}(\theta$-$\Omega,
\theta$-$\Omega)$. The preservation under several types of mappings of
$\alpha$-Hurewicz and $\theta$-Hurewicz properties are also discussed. Also, we
showed that, if $X$ is a mildly Hurewicz subspace of $ \omega^\omega$, than $X$
is bounded.
