The spin–lattice relaxation time T1 of the 19F nuclei was measured in gaseous samples of CF4, SiF4, GeF4, and SF6 at room temperature for densities from 0.015 to 20 amagat. In each case T1 was observed to pass through a minimum for some density less than 0.50 amagat. In addition, T1 was measured in the extreme narrowing region for SF6 at 238, 265, 293, 313, and 349.5 K.. The spin–rotation interaction provides the dominant relaxation mechanism in all cases. The data are analyzed on the basis of the assumption that the collision modulated spin–rotation interaction may be described by a single correlation function which is a simple exponential function of time. Values of an effective spin–rotation constant and a cross section for molecular reorientation are obtained for each gas. Assuming the validity of the model used to analyze the relaxation data, the combination of nuclear magnetic relaxation results with molecular beam measurements yields more accurate values of the anisotropic spin–rotation constant Cd than have been previously available.