  An $n$-dimensional manifold $M$ ($n\ge 3$) is called {\it generalized graph
manifold} if it is glued of blocks that are trivial bundles of $(n-2)$-tori
over compact surfaces (of negative Euler characteristic) with boundary. In this
paper two obstructions for generalized graph manifold to be nonpositively
curved are described.
  Each 3-dimensional generalized graph manifold with boundary carries a metric
of nonpositive sectional curvature in which the boundary is flat and geodesic
(B. Leeb). The last part of this paper contains an example of 4-dimensional
generalized graph manifold with boundary, which does not admit a metric of
nonpositive sectional curvature with flat and geodesic boundary.
