  Gravitational axial and chiral anomalies in a noncommutative space are
examined through the explicit perturbative computation of one-loop diagrams in
various dimensions. The analysis depend on how gravity is coupled to
noncommutative matter fields. Delbourgo-Salam computation of the gravitational
axial anomaly contribution to the pion decay into two photons, is studied in
detail in this context. In the process we show that the two-dimensional chiral
pure gravitational anomaly does not receive noncommutative corrections. Pure
gravitational chiral anomaly in 4k+2 dimensions with matter fields being chiral
fermions of spin-1/2 and spin-3/2, is discussed and a noncommutative correction
is found in both cases. Mixed anomalies are finally considered in both cases.
