  We consider the spin-exchange in ultracold collisions of hydrogen ($H$) and
antihydrogen ($\bar{H}$) atoms. The cross sections for transitions between
various hyperfine states are calculated. We show that the process of spin
exchange in $\bar{H}-H$ collisions is basically driven by the strong force
between proton and antiproton, that spin-exchange cross-sections are
proportional to the difference of singlet and triplet strong force S-wave
scattering lengths, while the strong force effects are enhanced about $10^9$
times due to long range atomic forces. We show that any difference in hyperfine
structure of $H$ and $\bar{H}$ (CPT violation) manifests itself in radical
change of spin-exchange cross-sections energy behavior.
