  Let $G$ be an algebraic group defined over a field $k$. We call $g\in G$ {\bf
real} if $g$ is conjugate to $g^{-1}$ and $g\in G(k)$ as {\bf $k$-real} if $g$
is real in $G(k)$. An element $g\in G$ is {\bf strongly real} if $\exists h\in
G$, $h^{2}=1$ (i.e. $h$ is an {\bf involution}) such that $hgh^{-1}=g^{-1}$.
Clearly, strongly real elements are real and are product of two involutions.
Let $G$ be a connected adjoint semisimple group over a perfect field $k$, with
-1 in the Weyl group. We prove that any strongly regular $k$-real element in
$G(k)$ is strongly $k$-real (i.e. is a product of two involutions in $G(k)$).
For classical groups, with some mild exceptions, over an arbitrary field $k$ of
characteristic not 2, we prove that $k$-real semisimple elements are strongly
$k$-real. We compute an obstruction to reality and prove some results on
reality specific to fields $k$ with $cd(k)\leq 1$. Finally, we prove that in a
group $G$ of type $G_2$ over $k$, characteristic of $k$ different from 2 and 3,
any real element in $G(k)$ is strongly $k$-real. This extends our results in
\cite{st}, on reality for semisimple and unipotent real elements in groups of
type $G_2$.
