  We investigate the constraints of dark matter search experiments on the
different candidates emerging from the minimal quasi-conformal strong coupling
theory with fermions in the adjoint representation. For one candidate, the
current limits of CDMS exclude a tiny window of masses around 120 GeV. We also
investigate under what circumstances the newly proposed candidate composed of a
-2 negatively charged particle and a $^4He^{+2}$ can explain the discrepancy
between the results of the CDMS and DAMA experiments. We found that this type
of dark matter should give negative results in CDMS, while it can trigger the
detectors of DAMA, if a condition between the mass and the binding energy of
the -2 particle with the nucleus of the detector is satisfied.
