This paper considers a natural generalization of the online list access problem in the paid exchange model, where additionally there can be precedence constraints ("dependencies") among the nodes in the list. For example, this generalization is motivated by applications in the context of packet classification. Our main contributions are constant-competitive deterministic and randomized online algorithms, designed around a procedure Move-Recursively-Forward, a generalization of Move-To-Front tailored to handle node dependencies. Parts of the analysis build upon ideas of the classic online algorithms Move-To-Front and BIT, and address the challenges of the extended model. We further discuss the challenges related to insertions and deletions.