  We derive the anomaly 8-form of 6-dimensional gauge theories arising in F
theory compactifications on elliptic Calabi-Yau threefolds. The result allows
to determine the matter content of certain such theories in terms of
intersection numbers on the base of elliptic fibration. We also discuss gauge
theories on 7-branes with double point singularities on the worldvolume.
Applications to Type II compactifications on Hirzebruch surfaces and $P^2$ are
outlined.
