A class of nonlinear time delay systems is characterized as differencedifferentially flat systems. For these the trajectory of any system variable can be calculated by solving a difference equation in which the “flat output” and its arbitrarily delayed derivatives occur as parameters. For algebraic delay systems a field theoretic characterization of difference-differential flatness is given, and a related concept of extended Brunovsky states is introduced. Using this concept linearizing predictive feedback can be designed. This is illustrated on the example of a chemical stirred tank reactor with a recycle loop modeled as a tubular reactor.