  We performed a search for a Lorentz-invariance- and CPT-violating coupling of
the $^3$He and $^{129}$Xe nuclear spins to posited background fields. Our
experimental approach is to measure the free precession of nuclear spin
polarized $^3$He and $^{129}$Xe atoms using SQUID detectors. As the laboratory
reference frame rotates with respect to distant stars, we look for a sidereal
modulation of the Larmor frequencies of the co-located spin samples. As a
result we obtain an upper limit on the equatorial component of the background
field $\tilde{b}^n_{\bot}< 8.4 \cdot 10^{-34}$ GeV (68\% C.L.). Furthermore,
this technique was modified to search for an electric dipole moment (EDM) of
$^{129}$Xe.
