  We compare the Hybrid Monte Carlo (HMC) and the Kramers equation algorithms
for simulations of QCD with two flavors of dynamical Wilson fermions and gauge
group $SU(2)$. The results for the performance of both algorithms are obtained
on $6^312$, $12^4$ and $16^4$ lattices at a pion to $\rho$ meson mass ratio of
$m_\pi/m_\rho \approx 0.9$. We find that the Kramers equation algorithm gives
an equally good performance as the HMC algorithm. We demonstrate that the
classical equations of motion used in these algorithms lack reversibility in
practical simulations and behave like those of a chaotic dynamical system with
a Liapunov exponent $\nu \approx 0.75$.
