The authors report solid-state {sup 13}C NMR measurements on powder samples of C{sub 60} and of a mixture of C{sub 60} and C{sub 70}. The NMR results show that, at 296 K, C{sub 60} molecules rotate rapidly and isotropically in the solid state, while C{sub 70} molecules rotate somewhat more anisotropically. These results are consistent with the proposed spherical geometry of C{sub 60} and prolate spheroidal geometry of C{sub 70}. The rotational correlation time of C{sub 60} molecules in the solid state becomes greater than 50 {mu}s at about 100 K.