The information economy, among other elements, heavily depends on cybersecurity. On the other hand, cybersecurity depends mainly on technology, on management procedures, on organizational structures, on law and on human competencies, to quote only some aspects of ICT security. To effectively sustain a coherent approach of cybersecurity, a national strategy, enforceable at a national level and compatible at the international level, should exist. This paper analyses some characteristics and issues related to the deployment of a national cybersecurity strategy in an interconnected world. It also points out the necessity of operational organizational structures and the importance of a cybersecurity culture to support a national cybersecurity strategy.