Kinetic rate laws arising from theoretical expectations for the oxidation of lipids initiated by water-soluble free radicals in compartmentalized systems under different experimental conditions are deduced. In particular, the predictions for the kinetic reaction orders in: (a) intra-particle oxidizable compound concentration (at fixed number of particles and particle size), α; (b) number of particles or analytical lipid concentration (at fixed intra-particle concentration and particle size), β and (c) initiator, γ, are obtained. The reaction orders β and γ are determined by the fraction of initiator derived radicals captured by the particles (f) and the mean number of chain carrying radicals per particle (<n>) when the system reaches the steady state condition. Predicted orders in initiator range from 0 (<n>=0.5) to 0.5 (f->1; <n>>>1), while the order in number of particles ranges between 0.5 (f->1; <n>>>1) and 1. These predictions are tested by measuring the kinetic law for the oxidation of SUV's egg yolk phosphatidylcholine vesicles initiated by the thermal decomposition of ABAP. The results indicate that, under the conditions employed, β=0.68+/-0.05 and γ=0.46+/-0.04. These values are close to those expected for a system in which <n>>>1 and the efficiency of capture is relatively high. This last condition is confirmed by estimating the efficiency of capture from a comparison of induction times elicited by similar concentrations of Trolox and α-tocopherol.