We model and analyze the secular evolution of stellar bars in spinning dark matter ( DM ) haloes with the cosmological spin \lambda \sim 0 - 0.09 . Using high-resolution stellar and DM numerical simulations , we focus on angular momentum exchange between stellar discs and DM haloes of various axisymmetric shapes — spherical , oblate and prolate . We find that stellar bars experience a diverse evolution which is guided by the ability of parent haloes to absorb angular momentum , J , lost by the disc through the action of gravitational torques , resonant and non-resonant . We confirm that dynamical bar instability is accelerated via resonant J -transfer to the halo . Our main findings relate to the long-term , secular evolution of disc-halo systems : with an increasing \lambda , bars experience less growth and basically dissolve after they pass through vertical buckling instability . Specifically , with increasing \lambda , ( 1 ) The vertical buckling instability in stellar bars colludes with inability of the inner halo to absorb J — this emerges as the main factor weakening or destroying bars in spinning haloes ; ( 2 ) Bars lose progressively less J , and their pattern speeds level off ; ( 3 ) Bars are smaller , and for \lambda \mathrel { \raise 1.29 pt \hbox { $ > $ } \mkern - 14.0 mu \lower 2.58 pt \hbox { $ \sim$ } % } 0.06 cease their growth completely following buckling ; ( 4 ) Bars in \lambda > 0.03 halos have ratio of corotation-to-bar radii , R _ { CR } / R _ { b } > 2 , and represent so-called slow bars without offset dust lanes . We provide a quantitative analysis of J -transfer in disc-halo systems , and explain the reasons for absence of growth in fast spinning haloes and its observational corollaries . We conclude that stellar bar evolution is substantially more complex than anticipated , and bars are not as resilient as has been considered so far .