Using the spin and flux evolution of the accreting pulsar 4U 1626-67 across the 2008 torque reversal, we determine the fastness parameter dependence of the dimensionless torque acting on the pulsar. We find that the dimensionless torque is qualitatively different from the existing models: it is concave-up across the torque equilibrium, whereas the existing torque models predict a concave-down (convex) relation with the fastness parameter. We show that the dimensionless torque has a cubic dependence on the fastness parameter near the torque equilibrium. We also find that the torque cannot attain large values away from the equilibrium, either in the positive or in the negative side, but saturates at limited values. The spin-down torque can attain a 2.5 times larger magnitude at the saturation limit than the spin-up torque. From the evolution of the frequency of quasi-periodic oscillations of 4U 1626-67 across the torque reversal of 1990, we determine the critical fastness parameter corresponding to torque equilibrium to bc omega(c) similar or equal to 0.75 within the framework of the beat frequency model and the boundary region model for reasonable values of the model parameters. We find that the disc magnetosphere interaction becomes unstable when the inner radius approaches the corotation radius as predicted by some models, though with a longer time-scale. We also find that there is an unstable regime that is triggered when the fastness parameter is 0.8 times the critical fastness parameter (omega = 0.6 for omega(c) similar or equal to 0.75) possibly associated with an instability observed in numerical simulations.