  Using spinorial geometry techniques, we classify the supersymmetric solutions
of euclidean ${\cal N}=4$ super Yang-Mills theory. These backgrounds represent
generalizations of instantons with nontrivial scalar fields turned on, and
satisfy some constraints that bear a similarity with the Hitchin equations, and
contain the Donaldson equations as a special subcase. It turns out that these
constraints can be obtained by dimensional reduction of the octonionic
instanton equations, and may be rephrased in terms of a selfduality-like
condition for a complex connection. We also show that the supersymmetry
conditions imply the equations of motion only partially.
