  As a continuation of \cite{NSY:local}, we mainly discuss the global structure
of two-dimensional locally compact geodesically complete metric spaces with
curvature bounded above. We first obtain the result on the Lipschitz homotopy
approximations of such spaces by polyhedral spaces. We define the curvature
measures on our spaces making use of the convergence of the curvature measures,
and establish Gauss-Bonnet Theorem. We also give a characterization of such
spaces.
