The effects of fuel stream dilution on the liftoff, stabilization, and blowout characteristics of laminar nonpremixed flames (NPFs) and partially premixed flames (PPFs) are investigated. Lifted methane-air flames were established in axisymmetric coflowing jets. Because of their flame suppression characteristics, two predominantly inert agents, CO2 and N2, were used as diluents. A time-accurate, implicit algorithm that uses a detailed description of the chemistry and includes radiation effects is used for the simulations. The predictions are validated using measurements of the reaction zone topologies and liftoff heights of both NPF and PPF. While an undiluted PPF is stabilized at the burner rim, characterized by significant radical destruction and heat loss to the burner, the corresponding undiluted NPF is lifted and stabilized in a low-velocity region extending from the wake of the burner. Detailed comparison of diluted NPF with PPF reveals that the base structures of both the flames are similar and exhibit a double flame structure in the near-field region, where the flame stabilization depends on a balance between the reaction rate and the scalar dissipation rate, which could also be interpreted as a balance between the edge-flame speed undergoing its local scalar dissipation rate and the local flow velocity. As diluent concentration is increased, the flames become weaker, move downstream along the stoichiometric mixture fraction line, and stabilize at a location where they can find a local flow field that has a lower scalar dissipation rate. Further increase of the diluent concentration moves the flames further downstream into the far-field region, where both the NPF and PPF exhibit a triple flame structure, and the flame stabilization mechanism also involves a balance between the triple flame speed and local flow velocity. The PPFs, however, shift to a higher liftoff height and blow out at a lower diluent concentration compared to the NPF, which can withstand larger amounts of dilution. In addition, both NPF and PPF are stabilized at lower liftoff heights and blowout at a lower diluent concentration, when they are diluted with N2 compared to that with CO2. The observed effects of fuel stream dilution and partial premixing on flame liftoff and blowout can be explained using the existing flame stabilization theories.