  The quantum theory of the mazer in the non-resonant case (a detuning between
the cavity mode and the atomic transition frequencies is present) is written.
The generalization from the resonant case is far from being direct. Interesting
effects of the mazer physics are pointed out. In particular, it is shown that
the cavity may slow down or speed up the atoms according to the sign of the
detuning and that the induced emission process may be completely blocked by use
of a positive detuning. It is also shown that the detuning adds a potential
step effect not present at resonance and that the use of positive detunings
defines a well-controlled cooling mechanism. In the special case of a mesa
cavity mode function, generalized expressions for the reflection and
transmission coefficients have been obtained. The general properties of the
induced emission probability are finally discussed in the hot, intermediate and
cold atom regimes. Comparison with the resonant case is given.
