  Let $f\colon M^{2n}\to\mathbb{R}^{2n+\ell}$, $n \geq 5$, denote a conformal
immersion into Euclidean space with codimension $\ell$ of a Kaehler manifold of
complex dimension $n$ and free of flat points. For codimensions $\ell=1,2$ we
show that such a submanifold can always be locally obtained in a rather simple
way, namely, from an isometric immersion of the Kaehler manifold $M^{2n}$ into
either $\mathbb{R}^{2n+1}$ or $\mathbb{R}^{2n+2}$, the latter being a class of
submanifolds already extensively studied.
