The rotational Zeeman effect spectra of 3-Fluoropyridine and 2,6-Difluoropyridine have been measured. The molecular <7-values are gaa = -0.0917(5), gbb = -0.0476(5), gC c = +0.0194(5) for 3-Fluoropyridine and gaa = -0.0573(6), gbb = -0.0311(6), gcc= + 0.0102(6) for 2,6-Difluoropyridine. The values for the magnetic susceptibility anisotropics in units of 10~6 erg/(G2 mol) are 2Xaa-\-Xbb + Xcc = 53.3(8), 2Xbb -Xcc -Xaa -60.5(7) for 3-Fluoropyridine and 2Xaa~X bb -_X "C C = 48.4(11), 2Xbb -XC c -X-aa = 51.7(11) for 2,6-Difluoropyridine. Subtraction of the local atom contributions to the magnetic susceptibilities indicates that Fluorine quenching of the nonlocal out of plane contribution depends on the position of the substituent. Further, the data suggest a linear correlation between Xj°nl0Cil and the "CNDO/2-7r-density alternation", which is used to predict susceptibility anisotropics of Fluorobenzenes and Fluoropyridines not yet mea sured.The molecular quadrupole moments are calculated from the Zeeman data and compared with the experimental values obtained for various fluorosubstituted Pyridines and Benzenes. If the quadrupole moments perpendicular to the molecular plane are referred to the centers of the six membered rings and are plotted against the number of Fluoroine substituents, n-p, the plots closely follow a straight line with identical slopes for the Pyridine-and Benzenefamilies, but with different intercepts at np = 0. From the "np = 0 intercept" for the Fluorobenzenes we conclude that the Benzene quadrupole moment proposed earlier by Shoemaker and Flygare should probably be revised.