For the linear system of functional-differential equations with bounded deviating argument the appropriate linear system of ordinary differential equations was built, all global solutions of which are global solutions of initial system. The construction of approximate system of differential equations was substantiated.

[1] Ryabov Yu.A. Application of the small parameter Lyapunov-Poincare method in the theory of systems with delay // Ing. journal. - 1961. - 1, issue 2. - P. 3-15. 2. Hale J. Theory of functional differential equations. - M.: Mir, 1984. - 421 p.

[2] Myshkis A.D. Linear differential equations with retarded argument. - M.: Nauka, 1972. - 352 p.

[3] Diblik J., Koksch N. Existence of global solutions of delayed differential equations via retract approach // Nonlinear Analysis. - 2006. - 64. - P. 1153 - 1170.

[4] Samoylenko A.M. On one problem of studying global solutions of differential equations with deviating argument // Ukr. mat. zhurn. - 2003.- 55, № 5.- P. 631-640.

[5] Sergeyeva L.M. Finding solutions to neutral-type differential equations with deviation of the argument / / Scientific Bulletin of Chernivtsi University: Collection of Scientific Works. Issue 421. Mathematics. - Chernivtsi: Ruta, 2008. - P. 96-100.

[6] Sergeyeva L.M. Finding solutions to neutral-type differential equations with deviation of the argument / / Scientific Bulletin of Chernivtsi University: Collection of Scientific Works. Issue 421. Mathematics. - Chernivtsi: Ruta, 2008. - P. 96-100.

[7] Samoilenko A.M., Perestyuk M.O., Parasyuk I.O. Differential Equations - Kyiv: Lybid, 2007. - 600 p.