The automatic identification and extraction of collocations from text corpora has become a popular research topic in computational lexicography. However, the mere statement that a given lexical unit bigram is a collocation is not sufficient for its inclusion into a collocation dictionary or its use in computational linguistics applications - for both, the specification of the semantics and syntactic structure of collocations is required. In this talk, we will present our work on the automatic classification of collocations with respect to the fine-grained lexico-semantic collocation typology provided by lexical functions. We will discuss the use of a variety of machine learning techniques and examine which linguistic criteria are pertinent for the task. Examples will be cited from experiments on Spanish and German material.