Diffusion-kinetic methods are used to investigate the effects of incident particle linear energy transfer (LET) on the radiolysis of water and aqueous solutions. Chemically realistic deterministic diffusion-kinetic calculations examining the scavenging capacity dependences of the scavenged yield of e(aq)(-) and of OH demonstrate that the scavenged yields are related to the underlying time-dependent kinetics in the absence of the scavenger by a simple Laplace transform relationship. This relationship is also shown to link the effect of an e(aq)(-) scavenger on the formation of H-2 with the time dependence of H-2 production in the absence of the scavenger. The simple Laplace relationship does not work well when applied to H2O2 formation in high-LET particle tracks even though such a relationship is valid with low-LET particles. It is found that while the secondary reaction of H2O2 with e(aq)(-) can be neglected in low-LET particle radiolysis, it is of considerable significance in the tracks produced by high-LET particles. The increased importance of this reaction with increasing LET is the major reason for the failure of the Laplace relationship for H2O2. It is also the cause of the larger yields of OH compared to e(aq)(-) at long times (small scavenging capacities). Analytic analyses using simple models show that the asymptotic time dependence of the kinetics of high-LET tracks is very different from that for low-LET tracks but is analogous to that for geminate pair recombination in two dimensions.