We use observations of the cosmological large-scale structure to derive limits on two-component hot dark matter consisting of mass-degenerate neutrinos and hadronic axions , both components having velocity dispersions corresponding to their respective decoupling temperatures . We restrict the data samples to the safely linear regime , in particular excluding the Lyman- \alpha forest . Using standard Bayesian inference techniques we derive credible regions in the two-parameter space of m _ { a } and \sum m _ { \nu } . Marginalising over \sum m _ { \nu } provides m _ { a } < 1.2 eV ( 95 % C.L . ) . In the absence of axions the same data and methods give \sum m _ { \nu } < 0.65 eV ( 95 % C.L . ) . We also derive limits on m _ { a } for a range of axion–pion couplings up to one order of magnitude larger or smaller than the hadronic value .