The main result of this paper is the construction of a minimal model for the function space
F
(
X
,
Y
)
\mathcal {F}(X,Y)
of continuous functions from a finite type, finite dimensional space
X
X
to a finite type, nilpotent space
Y
Y
in terms of minimal models for
X
X
and
Y
Y
. For the component containing the constant map,
π
∗
(
F
(
X
,
Y
)
)
⊗
Q
=
π
∗
(
Y
)
⊗
H
−
∗
(
X
;
Q
)
\pi _{*}(\mathcal {F}(X,Y))\otimes Q =\pi _{*}(Y)\otimes H^{-*}(X;Q)
in positive dimensions. When
X
X
is formal, there is a simple formula for the differential of the minimal model in terms of the differential of the minimal model for
Y
Y
and the coproduct of
H
∗
(
X
;
Q
)
H_{*}(X;Q)
. We also give a version of the main result for the space of cross sections of a fibration.