  We compute the $\widehat B_K$ parameter and the mass difference $\Delta
M_{LS}$ of the $K^0-\bar K^0$ system by means of the chiral quark model. The
chiral coefficients of the relevant $\Delta S=2$ and $\Delta S=1$ chiral
lagrangians are computed via quark-loop integration. We include the relevant
effects of one-loop corrections in chiral perturbation theory. The final result
is very sensitive to non-factorizable corrections of $O(\alpha_S N)$ coming
from gluon condensation. The size of the gluon condensate is determined by
fitting the experimental value of the amplitude $K^+ \to \pi^+\pi^0$. By
varying all the relevant parameters we obtain $\widehat{B}_K= 0.87 \pm 0.33\ .$
We evaluate within the model the long-distance contributions to $\Delta M_{LS}$
induced by the double insertion of the $\Delta S = 1$ chiral lagrangian and
study the interplay between short- and long-distance amplitudes. By varying all
parameters we obtain $\Delta M_{LS}^{th}/\Delta M_{LS}^{exp} = 0.76
^{+0.64}_{-0.34} .$ Finally, we investigate the phenomenological constraints on
the Kobayashi-Maskawa parameter Im $\lambda _t$ entering the determination of
$\epsilon'/\epsilon$.
