  We study the Stokes phenomenon for the solutions of general homogeneous
linear moment partial differential equations with constant coefficients in two
complex variables under condition that the Cauchy data are holomorphic on the
complex plane but finitely many singular or branching points with the
appropriate growth condition at the infinity. The main tools are the theory of
summability and multisummability, and the theory of hyperfunctions. Using them
we describe Stokes lines, anti-Stokes lines, jumps across Stokes lines, and a
maximal family of solutions.
