In this paper, a classification of combustion regimes is investigated for the diffusion flame of a hydrocarbon fuel jet in hot flue-gas co-flow (JHC) with varying oxygen fraction (up to 100%). Numerical simulations by computational fluid dynamics (CFD) are performed to obtain both forced-ignition and autoignition temperatures for the present investigation. All calculations use the Eddy Dissipation Concept (EDC) model with the well-known detailed chemistry-reaction mechanism of methane combustion (GRI-Mech 3.0). To validate the modeling, the predicted JHC flame characteristics are compared with those measured previously [Dally et al., Proc. Combust. Inst. 2002, 29, 1147-1154]. It is found that the predictions agree well with the measurements. Use of the predicted ignition temperatures can qualitatively classify the JHC combustion, based on previous suggestions [Cavaliere and de Joannon, Prog. Energy Combust. Sci. 2004, 30, 329-366] for combustion in a well-stirred reactor (WSR), into three distinct regimes: traditional combustion (TC), high-temperature combustion (HTC), and flameless combustion (FLC). The FLC regime can be further divided into three distinct zones. MILD (moderate or intense low-oxygen dilution), MILD-like, and quasi-MILD The MILD and MILD-like combustion regimes share the same necessary conditions proposed by Cavaliere and de Joannon while the quasi-MILD combustion does not. It is found that theoretically the MILD-like combustion should occur at any oxygen fraction, as long as the preheating temperature of co-flow prior to their reactions is sufficiently high. By comparison, all previous diffusion MILD combustions were established only for highly diluted reactants at an oxygen fraction of <10%. In this paper, a fundamental analysis of combustion regimes is provided generally for any combustion configuration.