  We show that a class of previously defined maps, called self-dual and causal
morphisms, form classical symmetries of Yang-Mills fields in four complex
dimensions. These maps generalize conformal transformations, and admit a
nonlocal pullback connection that preserves the equations of the theory. First
it is shown that self-dual morphisms form symmetries of the anti-self-dual
Yang-Mills equations under this pullback. Then a supersymmetric generalization
of causal morphisms is defined, which preserves solutions of the field
equations for N=3 supersymmetric Yang-Mills theory. As a special case, this
implies that a modified definition of causal morphisms form symmetries for the
ordinary Yang-Mills field equations.
