After recalling the definitions of the Abel-Radon transformation of currents and of locally residual currents, we show that the Abel-Radon transform $ℛ\left(\alpha \right)$ of a locally residual current $\alpha$ remains locally residual. Then a theorem of P. Griffiths, G. Henkin and M. Passare (cf. [7], [9] and [10]) can be formulated as follows  :Let $U$ be a domain of the grassmannian variety $G(p,N)$ of complex $p$-planes in ${\P }^N$, $U^{*}:={\cup }_{t\in U}{H}_t$ be the corresponding linearly $p$-concave domain of ${\P }^N$, and $\alpha$ be a locally residual current of bidegree $(N,p)$....