Abstract. In this paper we investigate the exponential stability of the trivial solution of the state-dependent delay differential equation $\dot x(t)=a(t)x(t-\tau(t,x(t)))$. It is shown that, under some conditions, this state-dependent equation is exponentially stable, if the trivial solution of $\dot y(t)=a(t)y(t-\tau(t,0))$ is exponentially stable. Assuming the existence of bounded partial derivatives of the delay function, the reverse statement will also be proved.

AMS Subject Classification (1991): 34K, 34D

Received March 22, 1999, and in revised form July 4, 1999. (Registered under 2722/2009.)