The relationship between the cross-sectional shape of W fibers and kinetic undercooling in directionally solidified (DS) NiAl-W eutectic alloys was investigated. When the growth rate was less than 8 A mu m/s, the cross-sectional shape of W fibers was hexagonal (faceted); conversely, when the growth rate was more than 8 A mu m/s, their cross-sectional shape was elliptical (nonfaceted). Meanwhile, the NiAl matrix and W fibers in DS NiAl-W eutectic alloys presented a particular crystallographic orientation. The crystallographic orientation between NiAl matrix and W fibers was [11](NiAl)//[200](W) in the growth rate of 6 A mu m/s, and [11](NiAl)//[11](W) in the growth rate of 8 A mu m/s. A critical kinetic undercooling can be used to predict the transition from the faceted to nonfaceted growth of W fibers in DS NiAl-W eutectic alloys. When the kinetic undercooling of the W phase was less than , the W fibers' growth was faceted with a hexagonal shape, whereas when , the W fibers exhibited nonfaceted growth with elliptical shape.