The nonlinear autonomous functional differential equation
x
˙
(
t
)
=
f
(
x
(
t
)
)
+
g
(
x
t
)
,
t
⩾
0
,
x
0
=
ϕ
\dot x(t) = f(x(t)) + g({x_t}),t \geqslant 0,{x_0} = \phi
is investigated by means of the theory of semigroups of nonlinear operators. The properties of the semigroup associated with this equation provide stability information about the solutions.