Spacetime scale-invariance and the super p-brane

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 ≠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.