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In this article we extend the framework of rough paths to processes ofvariable H\"older exponent or variable order paths. We show how a class ofmultiple discrete delay differential equations driven by signals of variableorder 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 drivingsignal, the local H\"older regularity of the variable order signal may be closeto 0, without more than C_{b}^{2} diffusion coefficients (in contrast to higherregularity requirements known from constant order rough path theory).Furthermore, we give a canonical algorithm to construct the iterated integralof variable order on the domain \left[0,T\right]^{2}, by constructing theiterated integrals on some well chosen strip around the diagonal of\left[0,T\right]^{2}, and then extending it to the whole domain using Chensrelation. At last, we give a recollection of the results of rough paths foundin [FriHai], but tailored for variable order paths.

Differential Equations Driven by Variable Order H\"older Noise, and the Regularizing Effect of Delay