We propose routes for the catalytic cycle and possible termination reactions for the polymerization of ethylene with cationic chromium complexes of the type [CpCr(L)R](+) which contain donor ligands with phosphorus or nitrogen (L = PR(3) or NR(3)). We confirm the rate-determining character of the insertion of ethylene into the chromium alkyl bond. Contrary to the situation with late transition metals, the resulting agostic isomers will readily isomerize. The termination of the polymerization reaction by beta-hydrogen elimination to the chromium center and subsequent dissociation of the resulting olefin is found to require about 25 kcal/mol and to be thermodynamically much less feasible than the alternative termination process by beta-hydrogen transfer to a monomer. The latter process involves spin change; two minimum-energy crossing points as well as further transition states and intermediates have been identified. Our calculations predict that adduct formation with the polymerization additive 9-BBN should be feasible both from a Cp-quinoline-based chromium catalyst and a zirconocene catalyst. However, only the latter undergoes exergonic chain transfer, which is in accordance with the experimentally observed formation of ultrahigh M(W) polyethylene when using 9-BBN as polymerization additive in combination with Cr catalysts. For the first time, quantum dynamics simulations of such open-shell systems have been performed, which give a lifetime of the Cr-alkyl complex with regard to ethylene insertion of only 500 fs. The simulations indicate that the dissociation of ethylene from the chromium center should be relatively insignificant compared to migratory insertion.