Bulk metallic glasses based on iron are known to possess very good soft magnetic properties due to their amorphous structure. The lack of crystallinity results in the very small magnetocrystalline anisotropy, minimising its contribution to the overall magnetic anisotropy. However, the presence of stress in the alloy, inevitable in the as-quenched state, may provoke magnetoelastic anisotropy. This factor may be reduced by either reduction of stress level by stress-relief annealing, or by modification of chemical composition in order to decrease the magnetostriction coefficient, λ. Specifically, if cobalt is added to an alloy for the improvement of its glass forming ability, magnetostriction is usually high, so the latter method may be inefficient. This work will show the efficiency of the stress relieving on the reduction of the coercive field of the studied materials, such as Fe-Co-(Ni)-Si-Nb-B and Fe-Co-Ni-Nb-Y-B glassy alloys.