2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62391We show a natural relation between the monodromy formula for focus-focus singularities of integrable Hamiltonian systems and a formula of Duistermaat-Heckman, and extend the main results of our previous note on focus-focus singularities ($\bbS^1$-action, monodromy, and topological classification) to the degenerate case. We also consider the non-Hamiltonian case, local normal forms, etc.final version, to appear in Lett. Math. PhysDynamical SystemsDifferential Geometry58F07,70H05text