The quantum theory of the two-photon mazer,previously limited to the degenerate case,is extended to the non-degenerate situation.The analytical expression for the atomic emission probability is obtained and the corresponding behavior is investigated.The results show that the emission probability behaviors in the non-degenerate two-photon mazer differ from those in the degenerate two-photon mazer,since two cavity modes are allowed in the mazer so that there are two freedoms changing the potentials that the atoms experience as they transit the cavity.