Robustness is a key issue for natural language processing in general and parsing in particular, and many approaches have been explored in the last decade for the design of robust parsing systems. Among those approaches is shallow or partial parsing, which produces minimal and incomplete syntactic structures, often in an incremental way. We argue that with a systematic incremental methodology one can go beyond shallow parsing to deeper language analysis, while preserving robustness. We describe a generic system based on such a methodology and designed for building robust analyzers that tackle deeper linguistic phenomena than those traditionally handled by the now widespread shallow parsers. The rule formalism allows the recognition of n-ary linguistic relations between words or constituents on the basis of global or local structural, topological and/or lexical conditions. It offers the advantage of accepting various types of inputs, ranging from raw to chunked or constituent-marked texts, so for instance it can be used to process existing annotated corpora, or to perform a deeper analysis on the output of an existing shallow parser. It has been successfully used to build a deep functional dependency parser, as well as for the task of co-reference resolution, in a modular way.