Disposal of spent nuclear fuel is a major political and public-perception problem for nuclear energy. From a radiological standpoint, the long-lived component of spent nuclear fuel primarily consists of transuranic (TRU) isotopes. Full recycling of TRU isotopes can, in theory, lead to a reduction in repository radiotoxicity to reference levels corresponds to the radiotoxicity of the unburned natural U required to fuel a conventional LWR in as little as ∼500 years provided reprocessing and fuel fabrication losses are limited. This strategy forms part of many envisaged ‘sustainable’ nuclear fuel cycles. However, over a limited timeframe, the radiotoxicity of the ‘final’ core can dominate over reprocessing losses, leading to a much lower reduction in radiotoxicity compared to that achievable at equilibrium. The importance of low reprocessing losses and minor actinide (MA) recycling is also dependent on the timeframe during which actinides are recycled. In this paper, the fuel cycle code ORION is used to model the recycle of light water reactor (LWR)-produced TRUs in LWRs and sodium-cooled fast reactors (SFRs) over 1–5 generations of reactors, which is sufficient to infer general conclusions for higher numbers of generations. Here, a generation is defined as a fleet of reactors operating for 60 years, before being retired and potentially replaced. Over up to ∼5 generations of full actinide recycle in SFR burners, the final core inventory tends to dominate over reprocessing losses, beyond which the radiotoxicity rapidly becomes sensitive to reprocessing losses. For a single generation of SFRs, there is little or no advantage to recycling MAs. However, for multiple generations, the reduction in repository radiotoxicity is severely limited without MA recycling, and repository radiotoxicity converges on equilibrium after around 3 generations of SFRs. With full actinide recycling, at least 6 generations of SFRs are required in a gradual phase-out of nuclear power to achieve transmutation performance approaching the theoretical equilibrium performance – which appears challenging from an economic and energy security standpoint. TRU recycle in pressurized water reactors (PWRs) with zero net actinide production provides similar performance to low-enriched-uranium (LEU)-fueled LWRs in equilibrium with a fleet of burner SFRs. However, it is not possible to reduce the TRU inventory over multiple generations of PWRs. TRU recycle in break-even SFRs is much less effective from a point of view of reducing spent nuclear fuel radiotoxicity.