We formulate an equation for the dynamic sedimentation of linear micelles (both rodlike and flexible) in the limit of local thermodynamic equilibrium when the recombination and scission of micelles are fast processes. A self-similar solution of the first kind is proposed for rodlike micelles in a free-draining approximation. The analytical structure of the associated nonlinear ordinary differential equation is very different from that pertaining to solutions of nonaggregating molecules. The theory may be of use in an experimental determination of the growth parameters by ultracentrifugation.