The equations of motion of the coupled electron-phonon system are integrated in real time for the model of polyacetylene recently proposed. To illustrate the physical behavior of this nonlinear system we consider the time evolution starting from three physically relevant configurations: (i) end generated soliton, (ii) electron-hole pair generation of a charged soliton-antisoliton pair, and (iii) the dressing of an injected electron. The calculations show that the system relaxes within a time of order 10(-13) sec, converting excited electron-hole pairs into soliton-antisoliton pairs.