  We describe a method of writing down interacting 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. The interaction equations
expressed in terms of loop variables, has a simple invariance that is exact
even off shell. A consistent definition of space-time fields requires the
fields to be functions of all the infinite number of gauge coordinates (in
addition to space time coordinates). The theory is formulated in one higher
dimension, where the modes appear massless. The dimensional reduction that is
needed to make contact with string theory (which has been discussed earlier for
the free case) is not discussed here.
