A linear system of differential equations with small parameter at a part of derivatives,a deviation of the argument,and a turning point

For a system of differential equations with small parameter at a part of derivatives, a linear deviation of the argument, and a turning point, we obtained conditions, under which its solutions are solutions of a system of differential equations with small parameter at a part of derivatives such that its matrices possess the asymptotic expansions at |ε| ≤ ε₀ with the coefficients holomorphic at |x| ≤ x ₀ . The existence and the infinite differentiability of a solution of the system of differential equations with small parameter at a part of derivatives and with a linear deviation of the argument in the presence of a turning point are proved.