We present some of the latest updated results on searches for
physics beyond the Standard Model at the Tevatron Collider using the full Run
1 data sample of ppbar collisions at sqrt s = 1.8 TeV collected with the CDF
and D0 detectors.  Results are reported relative to searches for squarks and
gluinos, scalar top and bottom quarks and superlight gravitino.  95% CL
exclusion limits are presented for degenerate states of Technicolor particles
p_T and rho_T.