Let
$X$
be a compact nonsingular real algebraic variety and let
$Y$
be either the blowup of
${{\mathbb{P}}^{n}}\left( \mathbb{R} \right)$
along a linear subspace or a nonsingular hypersurface of
${{\mathbb{P}}^{m}}\left( \mathbb{R} \right)\,\times \,{{\mathbb{P}}^{n}}\left( \mathbb{R} \right)$
of bidegree (1, 1). It is proved that a
${{\mathcal{C}}^{\infty }}$
map
$f:\,X\,\to \,Y$
can be approximated by regular maps if and only if
${{f}^{*}}\left( {{H}^{1}}\left( Y,\,{\mathbb{Z}}/{2}\; \right) \right)\,\subseteq \,H_{a\lg }^{1}\left( X,\,{\mathbb{Z}}/{2}\; \right)$
, where
$H_{a\lg }^{1}\left( X,\,{\mathbb{Z}}/{2}\; \right)$
is the subgroup of
${{H}^{1}}\left( X,\,{\mathbb{Z}}/{2}\; \right)$
generated by the cohomology classes of algebraic hypersurfaces in
$X$
. This follows from another result on maps into generalized flag varieties.