The annealing behavior of amorphous Co-Fe-B and Fe-B thin films, fabricated by rf sputtering in an argon plasma, have been investigated. The magnetostrictive Fe-B films exhibit a perpendicular anisotropy in the as-deposited condition, but after a stress relief anneal an in-plane anisotropy is obtained. An in-plane easy axis develops in the as-deposited Co-Fe-B thin films. The in-plane anisotropy direction in both sets of films can be rotated by annealing in an external magnetic field aligned parallel to the hard axis via a thermally activated process. Preannealing with a magnetic field aligned parallel to the easy axis stabilizes these films to a significant extent. The kinetics of easy axis rotation has a simple logarithmic dependence on time. Analysis of the kinetics of easy axis rotation indicates that preannealing apparently increases the thermal activation energy for this rotation process.