The shear-thickening behaviour of wormlike micelles, at concentrations just
below overlap, remains unexplained. In some cases, it has recently been co
nfirmed that very slow relaxations must be present even in the quiescent st
ate for example, the shear-thickening properties can depend on earlier ther
mal cycling. We present a speculative scenario based on the presence, just
below the ( apparent) overlap threshold, of large rings whose linking and d
elinking kinetics control the shear-thickening process. Equilibration betwe
en rings and open chains in turn controls the slow relaxations.