  We describe new $N$-extended 2D supergravities on a $(p+1)$-dimensional
(bosonic) space. The fundamental objects are moving frame densities that equip
each $(p+1)$-dimensional point with a 2D ``tangent space''. The theory is
presented in a $[p+1, 2]$ superspace. For the special case of $p=1$ we recover
the 2D supergravities in an unusual form. The formalism has been developed with
applications to the string-parton picture of $D$-branes at strong coupling in
mind.
