A numerical description of micellisation and relaxation to an aggregate equilibrium in nonionic surfactant solution with spherical premicellar aggregates and stable polydisperse cylindrical micelles is presented for wide interval of total surfactant concentrations and initial conditions. The Smoluchowsky-type model for the attachment-detachment rates of surfactant monomers to and from surfactant aggregates with matching the rates for small spherical premicellar aggregates and the rates for larger cylindrical micelles have been used. The full discrete spectrum of characteristic times of micellar relaxation and first three relaxation modes in their dependence on equilibrium monomer concentration have been computed with using the linearized form of the Becker-Döring difference equations. Overall time behavior of surfactant monomer and aggregate concentrations in micellisation and relaxation at large initial deviations from final equilibrium has been studied with the help of nonlinearized discrete Becker-Döring k