Static image theory for a homogeneous dielectric sphere was recently formulated by on the authors to account for the reaction of the sphere to the field from any electrostatic charge distribution. The theory is applied here in the analysis of the interaction of two dielectric spheres to find their reaction to external sources. Integral equations for the line image charges are formulated in the general case and a method for their solution is given in the limiting case of two conducting spheres. A simple, approximate dipole solution for the case of weak interaction between the spheres is also discussed. The theory has a potential application in analyzing interactions of closely packed spherical particles suspended in a host medium, in terms of one-dimensional integral equations.