  We generalize to p-dimensional extended objects and type II superstrings a
recently proposed Green-Schwarz type I superstring action in which the tension
$T$ emerges as an integration constant of the equations of motion. The action
is spacetime scale-invariant but its equations of motion are equivalent to
those of the standard super p-brane for $T\ne 0$ and the null super p-brane for
$T=0$. We also show that for $p=1$ the action can be written in ``Born-Infeld''
form.
