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Background The aim of the present study was to investigate the correlation between the triglyceride/glucose index (TyG index) and homeostasis model assessment of insulin resistance (HOMA-IR). Additionally, we compared the ability of the TyG index and triglycerides/high-density lipoprotein cholesterol (TG/HDL-c) index and the combination of these two indices (TyG index plus TG/HDL-c) to predict insulin resistance (IR) in South American overweight and obese children and adolescents. Methods A cross-sectional study was carried out in 345 overweight adolescents aged 10-18 years, from both the sexes. The TyG index was calculated as Ln (fasting triglycerides [mg/dL] × fasting glucose [mg/dL])/2, while the TG/HDL-c index was calculated by the division of TG (mg/dL) by HDL-c (mg/dL). HOMA-IR was calculated with the formula: fasting insulin (FI) (U/mL) × fasting glucose (mmol/L)/22.5. The cut-off point used to determine the presence of IR was HOMA-IR ≥ 3.16. Results The TyG index showed a positive correlation with HOMA-IR. The area under the receiver operating characteristic (ROC) curve of the TyG index was 0.74, indicating good sensitivity (75.7%) and specificity (67.4%). Furthermore, the TyG index cut-off point of >4.44 was established for IR prediction in this population. Conclusions The TyG index is a simple and cost-effective surrogate marker of IR in South American overweight children and adolescents. Moreover, due to its good accessibility, it can be used in large epidemiological studies.