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Introduction: Individual differences in heart rate variability (HRV) can be partly attributed to genetic factors that may be more pronounced during stress. Using data from the Oman Family Study (OFS), we aimed to estimate and quantify the relative contribution of genes and environment to the variance of HRV at rest and during stress; calculate the overlap in genetic and environmental influences on HRV at rest and under stress using bivariate analyses of HRV parameters and heart rate (HR)., Methods: Time and frequency domain HRV variables and average HR were measured from beat-to-beat HR obtained from electrocardiogram recordings at rest and during two stress tests [mental: Word Conflict Test (WCT) and physical: Cold Pressor Test (CPT)] in the OFS - a multigenerational pedigree consisting of five large Arab families with a total of 1326 participants. SOLAR software was used to perform quantitative genetic modelling., Results: Heritability estimates for HRV and HR ranged from 0.11 to 0.31 for rest, 0.09-0.43 for WCT, and 0.07-0.36 for CPT. A large part of the genetic influences during rest and stress conditions were shared with genetic correlations ranging between 0.52 and 0.86 for rest-WCT and 0.60-0.92 for rest-CPT. Nonetheless, genetic rest-stress correlations for most traits were significantly smaller than 1 indicating some stress-specific genetic effects., Conclusion: Genetic factors significantly influence HRV and HR at rest and under stress. Most of the genetic factors that influence HRV at rest also influence HRV during stress tests, although some unique genetic variance emerges during these challenging conditions.