  The existence of theta function solutions of genus two for the ILW equation
is established. A numerical example is also presented. The method basically
goes along with the Krichever's construction of theta function solutions for
soliton equations, such as the KP equation. This idea leads us to a question
whether a Riemann surface exists which allows a peculiar Abelian integral of
the third kind. The answer is affirmative at least for genus-two curves.
