Summary Chemical organisation theory has been proposed to provide a new perspective to study complex dynamical reaction networks. It decomposes a reaction network into over- lapping sub-networks called organisations. An organisation is an algebraically closed and self-maintaining set of molecular species. The set of organisations form a hierarchical “organisational structure”, which is here a lattice. In order to evaluate the usefulness of this approach we apply the theory to five models of immune response to HIV infection. We found four different lattices of organisations, which can be used as a first classification of the models. Furthermore, each organisation found can be assigned to a functional state of the system. And finally, the lattice of organisations can be used to ex- plain a treatment strategy on a more abstract level, i. e., as a movement from one organisation into another.