Families of amphiphilic oxidation-responsive polymers (poly(ethylene glycol)-polysulfides) with different architectures (linear, 4, 6, and 8-armed stars and 10, 15, and 20-armed combs) and compositions (variable ethylene sulfide/propylene sulfide ratio) are prepared. In water, all the polymers assemble in spherical micelles, with critical micellar concentrations <0.01 mg mL(-1) for all the branched polymers. Triple-detection gel permeation chromatography (GPC) and asymmetric field flow fractionation (AFFF) with dynamic and static light scattering detection, respectively, show an increasing compaction of the polymeric coil and a strong reduction of the aggregation number with increasing degree of branching. The key finding of this study is that the kinetics of the oxidative response sharply depend on the branching; in particular, it is highlighted that the degree of branching influences the lag time before a response can be observed rather than the speed of the response itself, a phenomenon that is attributed to a branching-dependent solubility of the oxidant in the polysulfide matrix.