The authors obtain exponential stability results for impulsive delay differential equations
where and . The approach is based on a reduction of the stability of (1), (2) to the solvability of a certain operator equation of second kind [cf. A. Anokhin, L. Berezansky and E. Braverman, J. Math. Anal. Appl. 193, No. 3, 923-941 (1995; Zbl 0837.34076)].