  We describe a method of writing down the exact interacting gauge invariant
equations for all the modes of the bosonic open string. It is a generalization
of the loop variable approach that was used earlier for the free, and lowest
order interacting cases. The generalization involves, as before, the
introduction of a parameter to label the different strings involved in an
interaction. The interacting string has thus becomes a ``band'' of finite
width. As in the free case, the fields appear to be massless in one higher
dimension. Although a proof of the consistency and gauge invariance to all
orders (and thus of equivalence with string theory) is not yet available,
plausibility arguments are given. We also give some simple illustrations of the
procedure.
