  The conditions of the traversable wormhole joining with the exterior
space-time are considered in details and the mixed boundary problem for the
Einstein equations is formulated. It is shown that, in opposite to some
declarations, the conditions of the wormhole joining with the exterior
space-time have non-dynamical nature and can not be defined by the physical
processes. The role of these conditions in the formation of the causal
structure of space-time is analyzed. It is shown that the causal structure of
the wormhole-type space-time models is independent from both the interior and
exterior energy-momentum tensors. This statement is illustrated in the
particular case of the spherical wormhole joining with flat exterior
space-time. The same conditions, which define the wormhole joining with the
exterior space-time, provide the absence of paradoxes in the models with
causality violation. It is pointed out, that the nature and physical
interpretation of the conditions of wormhole joining with the exterior
space-time and induced boundary conditions for the field variables is one of
the fundamental problems, which arise in the models with causality violation.
