We present a study of K0 and Lambda0 production in p anti-p
minimum-bias interactions at s**(1/2) = 1800 and 630 GeV.  Data is collected
by the CDF detector at the Tevatron collider.  Comparative analyses of
various inclusive distributions and correlations for the minimum-bias sample
as well as for the soft and hard subsamples are described at both the
available energies.