We present a thorough analysis of one- and two-color transient absorption measurements performed on single- and double-walled semiconducting carbon nanotubes. By combining the currently existing models describing exciton-exciton annihilation-the coherent and the diffusion-limited ones-we are able to simultaneously reproduce excitation kinetics following both E11 and E22 pump conditions. Our simulations revealed the fundamental photophysical behavior of one-dimensional coherent excitons and non-trivial excitation relaxation pathways. In particular, we found that after non-linear annihilation a doubly-excited exciton relaxes directly to its E11 state bypassing the intermediate E22 manifold, so that after excitation resonant with the E11 transition, the E22 state remains unpopulated. A quantitative explanation for the observed much faster excitation kinetics probed at E22 manifold, comparing to those probed at the E11 band, is also provided.