Abstract In the Bénard problem for two-fluid layers, Takens-Bogdanov bifurcations can arise when the stability thresholds for both layers are close to each other. In this paper, we provide an analysis of bifurcating solutions near such a Takens-Bogdanov point, under the assumption that solutions are doubly periodic with respect to a hexagonal lattice. Our analysis focusses on periodic solutions, secondary bifurcations from steady to periodic solutions and heteroclinic solutions arising as limits of periodic solutions. We compute the coefficients of the amplitude equations for a number of physical situations. Numerical integration of the amplitude equations reveals quasiperiodic and chaotic regimes, in addition to parameter regions where steady or periodic solutions are observed
