  We classify possible `self-duality' equations for p-form gauge fields in
space-time dimension up to D=16, generalizing the pioneering work of Corrigan
et al. (1982) on Yang-Mills fields (p=1) for D from 5 to 8. We impose two
crucial requirements. First, there should exist a 2(p+1)-form T invariant under
a sub-group H of SO(D). Second, the representation for the SO(D) curvature of
the gauge field must decompose under H in a relevant way. When these criteria
are fulfilled, the `self-duality' equations can be candidates as gauge
functions for SO(D)-covariant and H-invariant topological quantum field
theories. Intriguing possibilities occur for dimensions greater than 9, for
various p-form gauge fields.
