Monte Carlo simulations are used to investigate the effects of multiple ionization of water molecules on the yields of formation of free radical and molecular species, including molecular oxygen, in the radiolysis of pure, deaerated liquid water by using different types of radiation (H-1', He-4(2+), C-12(6+), and Ne-20(9+) ions) up to similar to 900 keV/mu m, at neutral pH and 25 degrees C. Taking into account the double, triple, and quadruple ionizations of water, the primary (or "escape") yields (at 10(-6) s) of the various radiolytic species (G(eaq)-, G(H)(.), G(H2), G(OH)(.), G(HO2)(.)/(O2)-, and G(H2O2)) are calculated as a function of the linear energy transfer (LET) of the radiation. Our results quantitatively reproduce the large increase observed in G(HO2)(.)/(.)(O2) at high LET. Under the conditions of this study, the mechanisms of triple and quadruple ionizations contribute only weakly to the production of kHO(2)(.)/O-2(.-). With the exception of protons, our calculations also simultaneously predict a maximum in G(H2O2) corresponding to the LET of similar to 4.5-MeV helium ions (similar to 100 keV/mu m) and similar to 110-MeV carbon ions similar to 180 keV/mu m). This maximum occurs where G(HO2)(/O2)(.)(.)- begins to rise sharply, suggesting, in agreement with previous experimental data, that the yields of HO2./O-2(.-) and H2O2 are closely linked. Moreover, our results show a steep increase in the initial and primary yields of molecular oxygen with increasing LET, giving support to the "oxygen in heavy-ion tracks" hypothesis. By contrast, it is found that, in the whole LET range considered, the incorporation of multiple ionization in the simulations has only little effect on the variation of our computed G(e)(ag)(-), G(H)(.), G(H2), and G(OH)(.) values as a function of LET. As expected, Ge-aq(-), and G(OH)(.) decrease continuously with increasing LET. G(H)(.) at first increases and then decreases at high LET. Finally, GH, monotonically rises with increasing LET. Our calculated yield values compare generally very well with experiment.