This paper proposes and compares two nonlinear time-domain models of self-excited thermoacoustic oscillations of laminar premixed flames. Both models are hybrid formulations, where the flame and its immediate vicinity are resolved with a reactive flow simulation, while the acoustic field is modeled with a low-order model that is coupled to the reactive flow simulation. Firstly, a flame model based on the fully compressible Navier-Stokes equations is investigated. In this case, the flame simulation is coupled to the low-order model via the characteristic wave amplitudes at the inlet boundary. Secondly, the flame is resolved with a low Mach number reactive flow simulation. In order to include two-way thermoacoustic feedback, this flame model is coupled with an acoustic network model via the global heat release rate and the fluctuation of the axial velocity at a reference position upstream of the flame. A bifurcation analysis using the plenum length as bifurcation parameter is conducted. Both models exhibit complex nonlinear oscillations and are in good agreement with each other. Therefore, we conclude that the coupling of a linear acoustic model and a nonlinear flame model via reference velocity and global heat release rate is sufficient to accurately capture thermoacoustic oscillations of the configuration investigated. This implies that the most important nonlinearities can be attributed to hydrodynamic effects and flame kinematics. Furthermore, the study corroborates that premixed flames respond predominantly to fluctuations of the upstream flow velocity. © 2016 by The Combustion Institute. Published by Elsevier Inc.