Applying Witten’s formula for global gauge and gravitational anomalies to 6-dimensional supergravities, we find: (a) The perturbatively anomaly free N=4 chiral supergravity coupled to 21 tensor multiplets is global anomaly free for any choice of space-time manifold with vanishing third Betti number (b3); (b) The perturbatively anomaly free matter coupled N=2 chiral super-gravities with arbitrary number of tensor multiplets, whose Yang-Mills gauge groups do not include G2, SU(2), or SU(3) are free of global anomalies if the theory is formulated on S6. In the case of 9 tensor multiplets coupled to supergravity, this result holds for any space-time with vanishing b3. (c) The N=6 chiral supergravity has perturbative gravitational anomalies and therefore the global anomalies need not be considered in this case.