  We construct the complete and explicit non-linear Kaluza-Klein Ansatz for
deriving the bosonic sector of the standard N=4 SO(4) gauged four-dimensional
supergravity from the reduction of D=11 supergravity on S^7. This provides a
way of interpreting all bosonic solutions of the four-dimensional gauged theory
as exact solutions in eleven-dimensional supergravity. We discuss certain
limiting forms of the Kaluza-Klein reduction, and compare them with related
forms in the Freedman-Schwarz N=4 SU(2)xSU(2) gauged theory. This leads us to
the result that the Freedman-Schwarz model is in fact a singular limiting case
of the standard SO(4) gauged supergravity. We show that in this limit, our
Ansatz for getting the SO(4) gauged theory as an S^7 reduction from D=11 indeed
reduces to an S^3 x S^3 reduction from D=10, which makes contact with previous
results in the literature. We also show that there is no distinction to be made
between having equal or unequal values for the gauge coupling constants $g$ and
$\tilde g$ of the two SU(2) gauge-group factors in the standard N=4 SO(4)
gauged supergravity, whilst by contrast the ratio of $g$ to $\tilde g$ is a
non-trivial parameter of the Freedman-Schwarz model.
