In this article, we propose the use of suffix arrays to efficiently implement n-gram language models with practically unlimited size n. This approach, which is used with synchronous back-off, allows us to distinguish between alternative sequences using large contexts. We also show that we can build this kind of models with additional information for each symbol, such as part-of-speech tags and dependency information. The approach can also be viewed as a collection of virtual k-testable automata. Once built, we can directly access the results of any k-testable automaton generated from the input training data. Synchronous back- off automatically identies the k-testable automaton with the largest feasible k. We have used this approach in several classification tasks.