For systems of linear functional differential equations (L FDE) we investigate the boundary value problems (BVP) both on a finite interval and on the real axis. We consider on a finit interval the BVPs for general system of L FDE and for system of linear ordinary differential equations with deviating argument (L ODE with DA): the Fredholmity and representation of solutions by Greens formula, the sign properties of a solution and prove the theorems of differential inequalities, the optimal, in a certain sense, conditions for the unique solvability (all the results are concretized for the initial, multi-point and periodic problems), the teorems on the well-possedness of above problems. For systems of L FDE and ODE with DA we consider the problems on existence of a periodic solution with a prescribed period and existence and unique existence of a bounded solution. Zdroj anotace: OKCZ - ANOTACE Z WEBU