Eustagger is a robust and wide-coverage morphological analyser and a Part-of-Speech tagger for Basque. The analyser is based on the two-level formalism and has been designed in an incremental way with three main modules: the standard analyser, the analyser of linguistic variants, and the analyser without lexicon which can recognize word-forms without having their lemmas in the lexicon. Using lexical transducers for our analyser we have improved both the performance of the different components of the system and the description itself. Provides possible lemmas, PoS and other morphological information for a token. It also recognizes date/time expressions, numbers. The methods we have used in disambiguation are Constraint Grammar formalism and an HMM based tagger. CG rules are applied using all the morphological features and this process decreases morphological ambiguity of texts. Finally, we use the stochastic tool to select just one from the possible remaining tags. Using only the stochastic method the error rate is about 14%, but the accuracy may be increased by about 2% enriching the lexicon with the unknown words. When both methods are combined, the error rate of the whole process is 3.5%.