The constraints on N=1 supergravities and type I superstrings from 2-loop chiral anomalies

N=1 supergravities with SO(22n+1) gauge groups are local chiral anomaly free at 1-loop in D=4n+2 dimensions (n≥0), as are SO(32) type I superstrings in 10D. We show that at 2-loops only D=6 and D=10 theories remain anomaly free, so a generalized Adler-Bardeen theorem continues to hold in these cases when the Green-Schwarz mechanism is used to cancel subleading and mixed anomalies.