Many tasks in computational linguistics can be regarded as configuration problems. In this paper, we introduce the notion of lexicalised multi-dimensional configuration problems (lmcps). This class of problems both has a wide range of linguistic applications, and can be solved in a straightforward way using state-of-the-art constraint programming technology. The paper falls into two main parts: We first present examples for linguistic configuration problems and show how to formalise them as constraint satisfaction problems. In the second part, we introduce Extensible Dependency Grammar (xdg), a framework for the development of linguistic resources in the context of lmcps.