The Run II physics programme of the Tevatron is proceeding with
more than 300 pb-1 of analysis quality data, collected at a centre-of-mass
energy of 1.96 TeV.  Searches for supersymmetric particles are starting to
set new limits, improving over the LEP and Run I results and exploring new
regions of parameter space.  We present recent results in Supersymmetry with
the upgraded CDF and D0 detectors and give some prospects for the future of
these searches.