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The Telecare project is a healthcare application aimed at minimizing the institutionalization of elderly people and patients with mobility problems and reducing the cost and burden of elderly care for the healthcare system. In this paper we investigate the utilisation of mobile ad hoc networks in the Telecare project from the view point of network security and information integrity, especially considering the fact that one main challenge in designing ad hoc networks is their vulnerability to security attacks, which is a major concern for many security sensitive applications. We have also looked at some of the threats that ad hoc network faces and the security goals to be achieved in the case of the Telecare system. Finally we have examined the main attributes of secure ad hoc networks in the light of the Telecare system, and discuss a possible solution through the use of public- key cryptography and digital signature approach.