The method of parametrization is used to obtain necessary and sufficient conditons for the correct solvability of the problem of finding the solution bounded on the entire real axis. For systems whose matrices and right-hand sides are constant in the limit, two-point bounary-value problems which approximate the problem in question are constructed. An estimate of the approximation is also given. The connection between the correct solvability of the original problem and that of the problem used as approximations is established.