The scalar nonlinear Volterra integral equation
\[
u
(
t
)
+
∫
0
t
g
(
t
,
s
,
u
(
s
)
)
d
s
=
f
(
t
)
(
0
⩽
t
)
u(t) + \int _0^t {g(t,s,u(s))\,ds = f(t)\qquad (0 \leqslant t)}
\]
is studied. Conditions are given under which the difference of two solutions can be estimated by the variation of the difference of the corresponding right-hand sides. Criteria for the existence of
lim
u
(
t
)
\lim u(t)
(as
t
→
∞
t \to \infty
) are given, and existence and uniqueness questions are also studied.