An exponential method for obtaining asymptotic expansions of the solution of a linear differential equation was presented by Brull and Soler in [3], We extend this method to the nonlinear differential equation of the type
L
(
u
)
+
Σ
1
N
f
(
x
,
t
)
u
n
=
0
L\left ( u \right ) + {\Sigma _1}^Nf\left ( {x, t} \right ){u^n} = 0
, where
t
t
is the small parameter. Three examples are used to illustrate the technique and to explain how uniformly valid expansions may be obtained.