  We complete the holomorphic anomaly equations for topological strings with
their dependence on open moduli. We obtain the complete system by standard path
integral arguments generalizing the analysis of BCOV (Commun. Math. Phys. 165
(1994) 311) to strings with boundaries. We study both the anti-holomorphic
dependence on open moduli and on closed moduli in presence of Wilson lines. By
providing the compactification a' la Deligne-Mumford of the moduli space of
Riemann surfaces with boundaries, we show that the open holomorphic anomaly
equations are structured on the (real codimension one) boundary components of
this space.
