Nearly quantum-limited Superconducting QUantum Interference Devices (S
QUIDs) have to be used in resonant mass gravitational wave antennas to
reach a displacement sensitivity of the order of 10(-21) m/root Hz in
a bandwidth of 100 Hz around the resonance frequency of about 900 Hz.
The design of these de SQUIDs will be described. The possible use of
Double Relaxation Oscillation SQUIDs (DROSs) was also studied. We show
that SQUIDs with a relatively large hole size can reach the quantum l
imit at low temperatures. The large hole size facilitates the coupling
between the SQUID and the inductive transformer circuit of the antenn
a.