Using system networks to build computational grammars is an alternative approach next to more formal frameworks (like e.g. HPSG in Stefan Mueller's BABEL-system). System networks constitute the core theory of systemic-functional linguistics (SFG). In my talk I will explain the work that I did during my internship at Language and Computing. I will explain how I developed a system in a system network grammar which handles ergativity in an efficient way. The grammar is constructed according to the principles of SFG (Halliday's IFG, 1994). I will also analyse ergativity within a conceptual system called Linkbase, a huge medical ontology developed at Language and Computing. The goal is to come up with a language-independent conceptual definition of ergativity, which can then be realised by an ergative pattern depending on the language in question.