Abstract: Semi-toric systems are completely integrable Hamiltonian systems on four dimensional symplectic manifolds characterised by the existence of a global Hamiltonian circle action and by the restriction on their singular fibres, which, loosely speaking, are either of the type that appear in the toric case or an analogue of nodal singularities of Lefschetz fibrations. Intuitively speaking, on the one hand, the rigidity coming from the circle action allows one to classify these systems (a result due to Pelayo and Vu Ngoc), while the presence of nodes makes the classification sufficiently richer than that of (closed) symplectic toric manifolds. The aim of this talk is to provide a different point of view on the classification semi-toric systems, trying to interpret the invariants constructed by Pelayo and Vu Ngoc as describing a singular integral affine structure. These (simple!) remarks have arisen from independent conversations with Rui Loja Fernandes, Eugene Lerman, Silvia Sabatini and Susan Tolman.