We discuss results of molecular dynamics computer simulation studies of 3 keV and 5 keV displacement cascades in β-SiC, and compare them to results of 5 keV cascades in pure silicon. The SiC simulations are performed with the Tersoff potential. For silicon we use the Stillinger-Weber potential. Simulations were carried out for Si recoils in 3 dimensional cubic computational cells with periodic boundary conditions and up to 175,616 atoms. The cascade lifetime in SiC is found to be extremely short. This, combined with the high melting temperature of SiC, precludes direct lattice amorphization during the cascade. Although large disordered regions result, these retain their basic crystalline structure. These results are in contrast with observations in pure silicon where direct-impact amorphization from the cascade is seen to take place. The SiC results also show anisotropy in the number of Si and C recoils as well as in the number of replacements in each sublattice. Details of the damage configurations obtained will be discussed.