  The need for modification of the Huygens-Fresnel superposition principle
arises even in the description of the free fields of massive particles and,
more extensively, in nonlinear field theories. A wide range of formulations and
superposition schemes for secondary waves are captured by Kirchhoff's integral
theorem. We discuss various versions of this theorem as well as its connection
with the superposition principle and the method of Green's functions. A
superposition scheme inherent in linear field theories, which is not based on
Kirchhoff's integral theorem but instead relies on the completeness condition,
is also discussed.
