  We describe covariant derivatives with respect to the coordinates of the full
superPoincar\'e group and dual coordinates, for Yang-Mills and supergravity.
The derivatives have engineering dimension running from 0 to 2. Prepotentials
appear as potentials for Lorentz derivatives (spin). Their role is clarified in
a lightcone analysis, where they also act as compensating gauge parameters and
Hertz potentials. Field strengths appear as potentials for dual-coordinate
derivatives, until dimensional reduction. These generalizations extend the
superstring's affine Lie algebra, and generalize gauge couplings for the
superparticle.
