BACKGROUND: Low-income and middle-income countries (LMICs) face major challenges in achieving the UN's Sustainable Development Goals (SDGs) for vulnerable adolescents. We aimed to test the UN Development Programme's proposed approach of development accelerators-provisions that lead to progress across multiple SDGs-and synergies between accelerators on achieving SDG-aligned targets in a highly vulnerable group of adolescents in South Africa. METHODS: We did standardised interviews and extracted longitudinal data from clinical records at baseline (2014-15) and 18-month follow-up (2016-17) for adolescents aged 10-19 years living with HIV in the Eastern Cape province of South Africa. We used standardised tools to measure 11 SDG-aligned targets-antiretroviral therapy adherence, good mental health, no substance use, HIV care retention, school enrolment, school progression, no sexual abuse, no high-risk sex, no violence perpetration, no community violence, and no emotional or physical abuse. We also assessed receipt at both baseline and follow-up of six hypothesised development accelerators-government cash transfers to households, safe schools (ie, without teacher or student violence), free schools, parenting support, free school meals, and support groups. Associations of all provisions with SDG-aligned targets were assessed jointly in a multivariate path model, controlling for baseline outcomes and sociodemographic and HIV-related covariates, and adjusted for multiple outcome testing. Cumulative effects were tested by marginal effects modelling. FINDINGS: 1063 (90%) of 1176 eligible adolescents were interviewed. Three provisions were shown to be development accelerators. Parenting support was associated with good mental health (odds ratio 2·13, 95% CI 1·43-3·15, p<0·0001), no high-risk sex (2·44, 1·45-5·03, p=0·005), no violence perpetration (2·59, 1·63-4·59, p<0·0001), no community violence (2·43, 1·65-3·86, p<0·0001), and no emotional or physical abuse (2·38, 1·65-3·76; p<0·0001). Cash transfers were associated with HIV care retention (1·87, 1·15-3·02, p=0·010), school progression (2·05, 1·33-3·24, p=0·003), and no emotional or physical abuse (1·76, 1·12-3·02, p=0·025). Safe schools were associated with good mental health (1·74, 1·30-2·34, p<0·0001), school progression (1·57, 1·17-2·13, p=0·004), no violence perpetration (2·02, 1·45-2·91, p<0·0001), no community violence (1·81, 1·30-2·55, p<0·0001), and no emotional or physical abuse (2·20, 1·58-3·17, p<0·0001). For five of 11 SDG-aligned targets, a combination of two or more accelerators showed cumulative positive associations, suggesting accelerator synergies of combination provisions. For example, the fitted probability of adolescents reporting no emotional or physical abuse (SDG 16.2) with no safe schools, cash transfers, or parenting support was 0·25 (0·16-0·34). With cash transfer alone it was 0·37 (0·33-0·42), with safe school alone 0·42 (0·30-0·55), and with parenting support alone 0·44 (0·30-0·59). With all three development accelerators combined, the probability of adolescents reporting no emotional or physical abuse was 0·76 (0·67-0·84). After correcting for multiple tests, four of the SDG-aligned targets (antiretroviral therapy adherence, no substance use, school enrolment, and no sexual abuse) were not associated with any hypothesised accelerators. INTERPRETATION: The findings suggest the UN's accelerator approach for this high-risk adolescent population has policy and potential financing usefulness. Services that simultaneously promote several SDG targets, or combine to support particular targets, might be important to meet not only health-related targets, but also to ensure that adolescents in LMICs thrive within a new development framework. FUNDING: Nuffield Foundation, UK Research and Innovation Global Challenges Research Fund, UKAID, Janssen Pharmaceutica, International AIDS Society, John Fell Fund, European Research Council, Economic and Social Research Council, Philip Leverhulme Trust, and UNICEF