**MSC:**- 34A37 Differential equations with impulses
- 34E05 Asymptotic expansions

physics, chemistry, biology, etc. . The development of the qualitative

theory of these systems is of particular interest since there solutions

can be found in an explicit form only in exceptional cases.

An efficient method by means of which the periodic solutions of differential equations are investigated

successfully is the method of a small parameter. In the present paper by means

of this method a periodic solution of a nonautonomous system of second

order impulsive differential equations is constructed. The case when the characteristic

equation has some complex conjugate roots is studied.