  First steps in incorporating Nottale's scale-relativity principle to string
theory and extended objects are taken. Scale Relativity is to scales what
motion Relativity is to velocities. The universal, absolute, impassible,
invariant scale under dilatations, in Nature, is taken to be the Planck scale
which is not the same as the string scale. Starting with Nambu-Goto actions for
strings and other extended objects, we show that the principle of
scale-relativity invariance of the world-volume measure associated with the
extended objects ( Lorentzian-scalings transformations with respect to the
resolutions of the world-volume coordinates) is compatible with the vanishing
of the scale-relativity version of the $\beta$ functions :
$\beta^G_{\mu\nu}=\beta^X=0$, of the target spacetime metric and coordinates,
respectively. Preliminary steps are taken to merge motion relativity with scale
relativity and, in this fashion, analogs of Weyl-Finsler geometries make their
appearance. The quantum case remains to be studied.
