BACKGROUND: Artemisinin-resistant genotypes of Plasmodium falciparum have now emerged a minimum of six times on three continents despite recommendations that all artemisinins be deployed as artemisinin combination therapies (ACTs). Widespread resistance to the non-artemisinin partner drugs in ACTs has the potential to limit the clinical and resistance benefits provided by combination therapy. We aimed to model and evaluate the long-term effects of high levels of partner-drug resistance on the early emergence of artemisinin-resistant genotypes. METHODS: Using a consensus modelling approach, we used three individual-based mathematical models of Plasmodium falciparum transmission to evaluate the effects of pre-existing partner-drug resistance and ACT deployment on the evolution of artemisinin resistance. Each model simulates 100 000 individuals in a particular transmission setting (malaria prevalence of 1%, 5%, 10%, or 20%) with a daily time step that updates individuals' infection status, treatment status, immunity, genotype-specific parasite densities, and clinical state. We modelled varying access to antimalarial drugs if febrile (coverage of 20%, 40%, or 60%) with one primary ACT used as first-line therapy: dihydroartemisinin-piperaquine (DHA-PPQ), artesunate-amodiaquine (ASAQ), or artemether-lumefantrine (AL). The primary outcome was time until 0·25 580Y allele frequency for artemisinin resistance (the establishment time). FINDINGS: Higher frequencies of pre-existing partner-drug resistant genotypes lead to earlier establishment of artemisinin resistance. Across all models, a 10-fold increase in the frequency of partner-drug resistance genotypes on average corresponded to loss of artemisinin efficacy 2-12 years earlier. Most reductions in time to artemisinin resistance establishment were observed after an increase in frequency of the partner-drug resistance genotype from 0·0 to 0·10. INTERPRETATION: Partner-drug resistance in ACTs facilitates the early emergence of artemisinin resistance and is a major public health concern. Higher-grade partner-drug resistance has the largest effect, with piperaquine resistance accelerating the early emergence of artemisinin-resistant alleles the most. Continued investment in molecular surveillance of partner-drug resistant genotypes to guide choice of first-line ACT is paramount. FUNDING: Schmidt Science Fellowship in partnership with the Rhodes Trust; Bill & Melinda Gates Foundation; Wellcome Trust.