For the nucleosynthesis of heavy and superheavy nuclei fission becomes very important when the r-process runs in a very high neutron density environment. In part, fission is responsible for the formation of heavy nuclei due to the inclusion of fission products as new seed nuclei (fission cycling). More than that, beta-delayed fission, along with spontaneous fission, is responsible in the late stages of the r-process for the suppression of superheavy element yields.For beta-delayed fission probability calculations a model description of the beta-strength- functions is required. Extended theoretical predictions for astro-physical applications were provided long ago, and new predictions also for superheavy nuclei with uptodate nuclear input are needed. For the further extension of data to heavier transactinides the models of strength- functions should be modified, taking into account more complicated level schemes. In our present calculations the strength-function model is based on the quasi-particle approximation of Finite Fermi Systems Theory.The probabilities of beta-delayed fission and beta-delayed neutron emission are calculated for some transfermium neutron-rich nuclei, and the influence of beta-delayed fission upon superheavy element formation is discussed.