  New reparametrisation invariant field equations are constructed which
describe $d$-brane models in a space of $d+1$ dimensions. These equations, like
the recently discovered scalar field equations in $d+1$ dimensions, are
universal, in the sense that they can be derived from an infinity of
inequivalent Lagrangians, but are nonetheless Lorentz (Euclidean) invariant.
Moreover, they admit a hierarchical structure, in which they can be derived by
a sequence of iterations from an arbitrary reparametrisation covariant
Lagrangian, homogeneous of weight one. None of the equations of motion which
appear in the hierarchy of iterations have derivatives of the fields higher
than the second. The new sequence of Universal equations is related to the
previous one by an inverse function transformation. The particular case of
$d=2$, giving a new reparametrisation invariant string equation in 3 dimensions
is solved.
