Past research suggests that the demands of information security policies (ISPs) cause stress upon employees, leading them to violate the policies. It emphasises the distress process but overlooks a possible positive process that may arise from the ISP demands (i.e., the eustress process) and motivate employees to reduce ISP violations. This study explores both the distress and eustress processes. It proposes that the challenge and hindrance aspects of ISP demands induce these processes and subsequently affect ISP violations. Besides, employees' ISP-related self-efficacy may facilitate or impede these processes. To test the research model, a survey was conducted on 375 employees in the U.S. The results show that the challenge aspect of ISP demands elicits a positive psychological response of employees, which in turn triggers their planful problem-solving to deal with these demands. In contrast, the hindrance aspect of ISP demands provokes a negative psychological response that triggers employees' wishful thinking about ISP demands. Meanwhile, employees' self-efficacy strengthens the effect of positive psychological response on planful problem-solving. Subsequently, planful problem-solving reduces employees' intention to violate the ISP, while wishful thinking increases their intention. This dual-process view sheds new light on the connection between ISP demands and ISP violation intention.