  We develop the BRST approach to Lagrangian construction for the massive
integer higher spin fields in an arbitrary dimensional AdS space. The theory is
formulated in terms of auxiliary Fock space. Closed nonlinear symmetry algebra
of higher spin bosonic theory in AdS space is found and method of deriving the
BRST operator for such an algebra is proposed. General procedure of Lagrangian
construction describing the dynamics of bosonic field with any spin is given on
the base of the BRST operator. No off-shell constraints on the fields and the
gauge parameters are used from the very beginning. As an example of general
procedure, we derive the Lagrangians for massive bosonic fields with spin 0, 1
and 2 containing total set of auxiliary fields and gauge symmetries.
