An existence and uniqueness result is given on the nonlinear Volterra equation
\[
u
(
t
)
+
(
a
∗
A
u
)
(
t
)
∍
f
(
t
)
,
t
∈
R
+
,
u(t) + (a ^\ast Au)(t) \backepsilon f(t),\quad t \in {R^ + },
\]
when considered in a real Hilbert space. The result extends earlier work by Barbu and Londen.