Three formulations of quasi-two-dimensional flamelet (Q2DF) models are derived from the two-dimensional flamelet formulation on the basis of assumptions regarding the third stream (diluent), and these models are validated by means of a two-dimensional direct numerical simulation (DNS) of a three-feed non-premixed combustion system into which the diluent is injected as the third stream. DNS combined with the Arrhenius formation (ARF) together with a detailed mechanism is also performed as a reference case and compared with the present models. The characteristics of the flamelets in three-feed non-premixed combustion are discussed in detail for ARF in terms of the three mixture fractions, temperature, and major and minor species. Some discrepancies appeared between the ARF and the Q2DF models. The difference in the cross-scalar dissipation rates between Q2DF and the two-dimensional flamelet model is considered the major reason for the deviations. The cross-scalar dissipation rates for the reactor streams and the diluent are expected to be either positive or negative values in the two-dimensional flamelet model, whereas only positive numbers resulted in the Q2DF cases. And the cross-scalar dissipation rate for the fuel and the oxidizer in the Q2DF models are always negative which is also varied from that in the two-dimensional flamelet model. As the results are not determined solely by a single mixture fraction, one scalar dissipation rate is insufficient for establishing a complete database, and it is considered that an additional scalar dissipation rate is needed to improve the model. Overall, it is confirmed that the three Q2DF models presented in this study capture the fundamental characteristics of flamelets in the three-feed non-premixed combustion system, although further improvement is required.