This numerical study investigates the combustion modes in the second stage of a sequential combustor at atmospheric and high pressure. The sequential burner (SB) features a mixing section with fuel injection into a hot vitiated crossflow. Depending on the dominant combustion mode, a recirculation zone assists flame anchoring in the combustion chamber. The flame is located sufficiently downstream of the injector resulting in partially premixed conditions. First, combustion regime maps are obtained from 0-D and 1-D simulations showing the co-existence of three combustion modes: autoignition, flame propagation and flame propagation assisted by autoignition. These regime maps can be used to understand the combustion modes at play in turbulent sequential combustors, as shown with 3-D large eddy simulations (LES) with semi-detailed chemistry. In addition to the simulation of steady-state combustion at three different operating conditions, transient simulations are performed: (i) ignition of the combustor with autoignition as the dominant mode, (ii) ignition that is initiated by autoignition and that is followed by a transition to a propagation stabilized flame, and (iii) a transient change of the inlet temperature (decrease by 150 K) resulting into a change of the combustion regime. These results show the importance of the recirculation zone for the ignition and the anchoring of a propagating type flame. On the contrary, the autoignition flame stabilizes due to continuous self-ignition of the mixture and the recirculation zone does not play an important role for the flame anchoring.