Abstract: This paper firstly investigates the distribution of the characteristic roots of singular differential systems with delay. It is pointed out that if all the
characteristic roots have negative real parts, under a condition, the maximal value of real parts of the characteristic roots is negative. This result shows that if all the characteristic roots have negative real parts, under a condition, the solution of singular differential systems with delay is exponentially stable. And finally, as an example, for the neutral differential systems, the conditions are given under which the solution is exponentially stable.

Key words: Singular differential systems with delay, Distribution of characteristic roots, Exponential stability