Recently, oxidative stress has been highlighted as a potential mediator underlying life-history trade-offs in animals. However, despite growing interest in the role of oxidative stress as a mechanistic explanation of trade-offs, the importance of oxidative stress in wild populations remain poorly understood. In this thesis, I use four commonly applied markers of oxidative stress. I apply two markers of oxidative damage, protein carbonyls and malondialdehyde, and two markers of antioxidant protection, superoxide dismutase activity and total antioxidant capacity. These were applied to samples collected in 2010-2013 and 2015 from the wild population of Soay sheep (Ovis aries), St Kilda, Scotland. I investigate correlations among different markers of oxidative stress, and their within individual repeatability over time. In addition, I examine the role played by oxidative stress in mediating life-history traits at different life-stages; specifically, I test for associations between oxidative stress, growth and survival in Soay sheep lambs. I also investigate the oxidative costs of reproduction in adult Soay sheep females and I test whether any such costs vary with age. My findings reveal, firstly, that plasma markers of oxidative stress vary dramatically among years, and that the different markers of oxidative damage and antioxidant protection applied throughout this thesis, are uncorrelated with each other (Chapter 2). This indicates that oxidative stress is a multifaceted process, where each oxidative stress marker may reflect different and potentially uncoupled biochemical processes (Chapter 2). Second, faster lamb growth shows a weak, positive association with malondialdehyde. However, growth is not associated with variation in the other three markers (Chapter 3). In addition, lamb survival also shows marker dependent associations; lambs with higher superoxide dismutase activity are more likely to survive their first winter, as are male but not female lambs with lower protein carbonyl content. Survival does not vary with malondialdehyde or antioxidant capacity. Thus, different markers of oxidative stress capture different aspects of the complex relationships between individual oxidative state, physiology and fitness (Chapter 3). Third, protein carbonyl content and superoxide dismutase activity measured at birth and at four month old in the lambs, show no within individual repeatability, although there is a significant difference in mean marker values over time (Chapter 4). This indicates that these markers of oxidative stress might reflect transient, rather than general, physiological states. Finally, I find some evidence for an oxidative cost of reproduction and for age-related variation in oxidative stress (Chapter 5). However, once again, effect are highly marker and year dependent, and I find no consistent patterns of variation across the two oxidative damage markers or across the two antioxidant protection markers, as they all show different responses to both breeding and age (Chapter 5). Together, my results provide some support for the association between oxidative stress and life-histories, but the effects are both marker and year dependent. Furthermore, the lack of correlation among different markers and the lack of within individual repeatability of oxidative stress markers highlight the need for careful selection and interpretation of plasma oxidative stress markers in the wild.