  In this article we extend the framework of rough paths to processes of
variable H\"older exponent or variable order paths. We show how a class of
multiple discrete delay differential equations driven by signals of variable
order are especially well suited to be studied in a path wise sense. In fact,
under some assumptions on the H\"older regularity functions of the driving
signal, the local H\"older regularity of the variable order signal may be close
to 0, without more than C_{b}^{2} diffusion coefficients (in contrast to higher
regularity requirements known from constant order rough path theory).
Furthermore, we give a canonical algorithm to construct the iterated integral
of variable order on the domain \left[0,T\right]^{2}, by constructing the
iterated integrals on some well chosen strip around the diagonal of
\left[0,T\right]^{2}, and then extending it to the whole domain using Chens
relation. At last, we give a recollection of the results of rough paths found
in [FriHai], but tailored for variable order paths.
