We study with an ab initio molecular dynamics method the bond-breaking and bond-forming processes in chemical reactions. To obtain reactive trajectories, we use a newly developed method based on the optimization of a suitably defined action. The Hellmann-Feynman forces, which are needed to optimize the action, are calculated within density-functional theory. We contrast a concerted [4+2] cycloaddition of cyclopentadiene and ethylene with the nonconcerted [2+2] cycloaddition of two ethylene molecules. We find that the duration of the bond-breaking and bond-forming processes due to the nuclear motion is similar to100 fs. Moreover the electronic delocalization, as well as the HOMO-LUMO energy gap during the two reactions, allows us to distinguish clearly between the concerted and the nonconcerted mechanism.