The nonstationary dynamics of the heliospheric termination shock in the presence of pickup ions (PUI) is analyzed by using a one-dimensional particle-in-cell simulation code. This work initially stimulated by Voyager 2 data focusses on this nonstationarity for different percentages of PUIs and for different Alfvén Mach numbers M A. Solar wind ions (SWIs) and PUIs are described, respectively, as Maxwellian and shell distributions (with a zero/finite thickness). For a moderate M A, present results show that (1) the shock front is still nonstationary even in the presence of 25% of PUIs; its instantaneous velocity varies, which is in favor for shock multicrossing; (2) the presence of PUIs tends to smooth out the time fluctuations of field amplitude and of microstructure widths at the front and overshoot; (3) the shock has a multiple overshoot, which is analyzed by identifying the contributions of SWIs and the PUIs; (4) as the PUI percentage increases, the shock moves faster and the downstream compression becomes weaker, which is explained by a Rankine–Hugoniot model; (5) the reflection rate of SWIs and PUIs decreases as the PUI percentage increases; (6) the shock structure is almost insensitive to the shell thickness; and (7) for the PUIs dominated shock case (PUI = 55%), the shock becomes stationary. However, for higher M A regime, the front nonstationarity persists even in the PUI = 55% case. In summary, high M A regime allows to compensate the smoothing of the microstructures and the time fluctuations of the shock front brought by the presence of PUIs.