This paper describes the representation of Basque Multiword Lexical Units and the automatic processing of Multiword Expressions. After discussing and stating which kind of multiword expressions we consider to be processed at the current stage of the work, we present the representation schema of the corresponding lexical units in a general-purpose lexical database. Due to its expressive power, the schema can deal not only with fixed expressions but also with morphosyntactically flexible constructions. It also allows us to lemmatize word combinations as a unit and yet to parse the components individually if necessary. Moreover, we describe HABIL, a tool for the automatic processing of these expressions, and we give some evaluation results. This work must be placed in a general framework of written Basque processing tools, which currently ranges from the tokenization and segmentation of single words up to the syntactic tagging of general texts.