‘Deep-syntactic’ dependency structures that capture the argumentative, attributive and coordinative relations between full words of a sentence have a great potential for a number of NLP-applications. The abstraction degree of these structures is in between the output of a syntactic dependency parser (connected trees defined over all words of a sentence and language-specific grammatical functions) and the output of a semantic parser (forests of trees defined over individual lexemes or phrasal chunks and abstract semantic role labels which capture the frame structures of predicative elements and drop all attributive and coordinative dependencies). We propose a parser that provides deep-syntactic structures. The parser has been tested on Spanish, English and Chinese.