Appendices were not supplied with the digital version of the thesis but are available in the print version. / The present research includes two studies. Study I was based on the research finding that exposure to nuclear radiation and other toxic chemicals results in those who were exposed not only believing their health to be affected, but experiencing significant and chronic stress. It was hypothesised that ongoing stress for New Zealand’s nuclear test veterans resulting from the inability to adapt to their past nuclear exposure would result in them experiencing greater depressive symptomatology, poorer perceived health, and poorer perceived memory performance than a control group. Psychological profiles of 50 nuclear test veterans and 50 age-matched Control participants were obtained through postal survey and face-to-face interview, using the Geriatric Depression Scale, Medical Outcomes Study Short Form-36, and the Memory Assessment Clinics Self-Rating Scale. As predicted, the nuclear veterans exhibited more depressive symptoms, and perceived their health and memory performance to be poorer than the Control group. A stress theory framework is applied to help conceptualise the experience of the nuclear veterans, and to provide an explanation for their lower scores and consequent poorer functioning. Through the pathway of poor perceived health leading to anxiety, health anxiety was considered a form of chronic stress the nuclear veterans were experiencing. Consequently, Study II aimed to examine whether Acceptance and Commitment Therapy (ACT) could be usefully applied to relieve this anxiety. Most psychotherapeutic approaches have been developed for problems that have an "irrational" or "pathological" foundation. However, these approaches often fit poorly with psychological distress that stems from cognitions that are reality-based and may need to be accepted rather than changed, such as in the case of nuclear exposure-related health anxiety. ACT may be particularly useful in these situations in which cognitive change is not warranted. Study II examined the use of ACT with 5 NZ nuclear test veterans (of either Māori or Pākehā descent) experiencing moderate to high levels of health anxiety. Results of self-report measures administered at baseline, during treatment, post-treatment, and at 6-week follow-up indicated varying results amongst these men. One participant showed clinically significant post-treatment reductions in health anxiety, experiential avoidance, and general psychological distress that were maintained at follow-up. Two participants showed clinically significant post- vi treatment reductions in health anxiety, experiential avoidance, and distress, despite not engaging in therapy as they did not wish to make changes. For the same reason, a fourth participant chose not to engage in therapy, despite high baseline scores on all measures, and showed no improvement during or after therapy. The fifth participant had low baseline scores on all measures, maintaining these throughout therapy, and at follow-up. Results are explained in terms of cohort and gender effects, with suggestions for adapting ACT with NZ older adults, particularly males. Implications for the utility of ACT with toxic exposure populations, older adults, and various cultures are discussed.