  We present a new general topological tensor current of $\tilde{p}$-branes by
making use of the $\phi $-mapping theory. It is shown that the current is
identically conserved and behave as $\delta (\vec{\phi}),$ and every isolated
zero of the vector field $\vec{\phi}(x)$ corresponds to a `magnetic'
$\tilde{p}$-brane. Using this topological current, the generalized Nambu action
for multi $\tilde{p}$-branes is given, and the field strength $F$ corresponding
to this topological tensor current is obtained. It is also shown that the
`magnetic' charges carried by $\tilde{p}$-branes are topologically quantized
and labeled by Hopf index and Brouwer degree, the winding number of the
$\phi$-mapping.
