Liapunov functionals of quadratic form have been used extensively for the study of the stability properties of linear ordinary, functional and partial differential equations. In this paper, a quadratic functional
V
V
is constructed for the linear Volterra integrodifferential equation
\[
x
˙
(
t
)
=
A
x
(
t
)
+
∫
0
T
B
(
t
−
τ
)
x
(
τ
)
d
t
,
t
≥
t
0
,
x
(
t
)
=
f
(
t
)
,
0
≤
t
≤
t
0
\dot x\left ( t \right ) = Ax\left ( t \right ) + \int _0^T {B\left ( {t - \tau } \right )x\left ( \tau \right ) dt, \qquad t \ge {t_0}, \\ x\left ( t \right ) = f\left ( t \right ), \qquad 0 \le t \le {t_0}}
\]
. This functional, and its derivative
V
˙
\dot V
, is more general than previously constructed ones and still retains desirable computational qualities; moreover, it represents a natural generalization of the Liapunov function for ordinary differential equations. The method of construction used suggests functionals which are useful for more general equations.