The isothermal anelastic deformation below the glass transition temperature T-g was investigated on Fe40Ni40B20 and Ni77.5Si7.5B15 amorphous ribbons. Experiments were carried out at temperatures 320 and 340 degrees C after application of mechanical stress steps between 5 - 210 MPa. The obtained anelastic deformation data have been analyzed using two different methods to calculate the relaxation time and activation energy spectrum. Both of these methods reveal that the anelastic relaxation processes in the amorphous structure strongly depend on chemical composition, cooling rate and structural relaxation state of the amorphous structure. The obtained spectra involve three or four quite well separated peaks, each of them represents a different mode of a local atomic rearrangement during the anelastic deformation.