  We present a systematic study of the spectral consequences of departures from
chemical equilibrium in the atmospheres of L and T dwarfs, and for even cooler
dwarfs. The temperature/pressure profiles of the non-equilibrium models are
fully consistent with the non-equilibrium chemistry. Our grid of
non-equilibrium models includes spectra for effective temperatures from 200 K
to 1800 K, three surface gravities, four possible values of the coefficient of
eddy diffusion in the radiative zone, and three different CO/CH$_4$ chemical
reaction prescriptions. We find that the non-equilibrium overabundance of CO
translates into flux suppressions in the M ($\sim4-$5 $\mu$m) band of at most
$\sim$40% between effective temperatures of 600 and 1800 K. The effect is
largest around $T_{\rm eff} \approx 1100$ K. The underabundance of ammonia due
to non-equilibrium chemistry translates into flux enhancements of no more than
$\sim$20% for the $T_{\rm eff}$ range from 300 to 1800 K, with the largest
effects at the lowest values of $T_{\rm eff}$. The magnitude of the departure
from chemical equilibrium increases with decreasing gravity, with increasing
eddy diffusion coefficient, and with decreasing speed of the CO/CH$_4$
reaction. Though these effects are modest, they lead to better fits with the
measured T dwarf spectra. Furthermore, the suppression in the M band due to
non-equilibrium enhancements in the CO abundance disappears below $\sim$500 K,
and is only partial above $\sim$500 K, preserving the M band flux as a useful
diagnostic of cool atmospheres and maintaining its importance for searches for
brown dwarfs cooler than T dwarfs.
