Transient absorption traces taken on samples of the polymer MEH-PPV are measured as a function of the laser intensity. In increasing the laser power, different decay dynamics of the signal are obtained. This suggests that effective exciton-exciton annihilation takes place. The signals are interpreted using a microscopic quantum mechanical model. The analysis points at an ultrafast excitonic decay via interchain and intrachain annihilation, where the latter process is roughly thirty times slower. Afterwards, diffusion-induced annihilation and relaxation become effective and thus determine the long-time behavior of the excited-state decay.