  In this paper, we start by proving the existence of the strict transform of a
positive current $T$ as soon as its $j^{th}$ currents, $T_j$, are
plurisubharmonics or plurisuperharmonics. Then, with a suitable condition on
$T_j$, we show the existence of the directional tangent cone to $T$. In the
particular case, when $T$ is closed, we give a second condition independent to
the previous one.
