Amorphous Fe78Si9B13 and (FeNiCr)78 (SiB)22 ribbons and their composite ribbons were made by a double-chamber-crucible technique. Ms-T curves and hysteresis loops of the lap-wound-cores of the two ribbons and composite ribbons were measured. The hysteresis loop of the lap-wound-cores was waist-like, and was closed but not equal to the average of the two components. For the composite ribbon cores, their Ms-T curve was practically the average of the two components. However, their hysteresis loop was no longer waist-like, but a flat one. These changes of the hysteresis loops of the lap-wound-cores and composite cores were suggested to result from the internal stress induced by the difference of the thermal expansion and magneto-striction of the two components.