Tagging is the task of attributing to words in context in a text, their corresponding Part-of-Speech (PoS) class. In this work, we have employed Variable Length Markov Chains (VLMC) for tagging, in the hope of capturing long distance dependencies. We obtained one of the best PoS tagging of Portuguese, with a precision of 95.51%. More surprisingly, we did that with a total time of training and execution of less than 3 minutes for a corpus of almost 1 million words. However, long distance dependencies are not well captured by the VLMC tagger, and we investigate the reasons and limitations of the use of VLMCs. Future researches in statistical linguistics regarding long range dependencies should concentrate in other ways of solving this limitation.