  We discuss the issue of global anomalies in chiral gauge theories on the
lattice. In Luscher's approach, these obstructions make it impossible to define
consistently a fermionic measure for the path integral. We show that an SU(2)
theory has such a global anomaly if the Weyl fermion is in the fundamental
representation. The anomaly in higher representations is also discussed. We
finally show that this obstruction is the lattice analogue of the SU(2) anomaly
first discovered by Witten.
