Premixed staged combustion in gas-turbine combustors, where a premixed fuel-air mixture is injected into a hot vitiated environment, has promise for better emission control. In these hot environments that occur at high engine pressure, the flames may stabilize by a combination of autoignition and premixed flame propagation. In this work, a laminar and steady premixed jet in vitiated coflow was studied numerically to examine the stability behavior of such flames that are impacted by both autoignition and flame propagation. Simulations with detailed chemistry were used with boundary conditions matching previous experiments to understand the stability mechanisms. At the conditions studied, the laminar flame was lifted, with the region of highest heat release rates occurring downstream of the jet exit. However, nonzero heat release rates an order-of-magnitude below the maximum value were observed continuously to the jet exit. An energy budget analysis was conducted along streamlines through different portions of the flame. Streamlines flowing through relatively low heat release rate regions near the burner exit were only influenced by mixing between the jet and vitiated coflow. Streamlines which flowed through higher heat release rates in the lifted flame were influenced by heat transfer from both the coflow and the existing flame, leading to heat-transfer assisted propagating premixed-flame behavior. Species budgets analyzed in the low- and high-heat release regions of the flames were also used to characterize autoignition locations. The species budget through autoignition regions showed clear markers such as high CH2O concentrations present ahead of high heat release rates. The streamlines through premixed propagation regions of the flame also had high CH2O concentrations upstream of the high heat release region, but the species budget shows this is due to mixing from autoignition regions as opposed to reactions occurring on the streamline ahead of the flame. Thus, caution must be taken when using CH2O as a marker for autoignition in such flames with mixed stabilization modes. (C) 2020 The Combustion Institute. Published by Elsevier Inc. All rights reserved.