  Some problems of the space-time causal structure are discussed using models
with traversable wormholes. For this purpose the conditions of traversable
wormhole matching with the exterior space-time are considered in detail and a
mixed boundary problem for the Einstein equations is formulated and analyzed.
The influence of these matching conditions on the space-time properties and
causal structure is analyzed. These conditions have a non-dynamical nature and
cannot be determined by any physical process. So, the causality violation
cannot be a result of dynamical evolution of some initial hypersurface. It is
also shown that the same conditions which determine the wormhole joining with
the outer space provide the self-consistency of solutions and the absence of
paradoxes in the case of causality violation.
