  We present some results of the calculation of MSSM one-loop contributions to
strong $t \bar t$ production in hadronic collisions. Here we concentrate on the
MSSM electroweak-like O(\alpha) and SQCD O(\alpha_s) corrections to the main
production mechanism at the Fermilab Tevatron $p \bar p$ collider, $q\bar q\to
g \to t \bar t$. We give results for the total $t \bar t$ production rate and
for parity violating asymmetries in the production of left and right handed top
quark pairs.
