In this paper the methods of rational homotopy theory are applied to a family of examples from singularity theory. Let
A
{\mathbf {A}}
be a finite collection of hyperplanes in
C
l
{{\mathbf {C}}^l}
, and let
M
=
C
l
−
⋃
H
∈
A
H
M = {{\mathbf {C}}^l} - \bigcup \nolimits _{H \in {\mathbf {A}}} H
. We say
A
{\mathbf {A}}
is a rational
K
(
π
,
1
)
K(\pi ,\,1)
arrangement if the rational completion of
M
M
is aspherical. For these arrangements an identity (the LCS formula) is established relating the lower central series of
π
1
(
M
)
{\pi _1}(M)
to the cohomology of
M
M
. This identity was established by group-theoretic means for the class of fiber-type arrangements in previous work. We reproduce this result by showing that the class of rational
K
(
π
,
1
)
K(\pi ,\,1)
arrangements contains all fiber-type arrangements. This class includes the reflection arrangements of types
A
l
{A_l}
and
B
l
{B_l}
. There is much interest in arrangements for which
M
M
is a
K
(
π
,
1
)
K(\pi ,\,1)
space. The methods developed here do not apply directly because
M
M
is rarely a nilpotent space. We give examples of
K
(
π
,
1
)
K(\pi ,\,1)
arrangements which are not rational
K
(
π
,
1
)
K(\pi ,\,1)
for which the LCS formula fails, and
K
(
π
,
1
)
K(\pi ,\,1)
arrangements which are not rational
K
(
π
,
1
)
K(\pi ,\,1)
where the LCS formula holds. It remains an open question whether rational
K
(
π
,
1
)
K(\pi ,\,1)
arrangements are necessarily
K
(
π
,
1
)
K(\pi ,\,1)
.