Based on the results of the information and communications technologies (ICTs), a new “digital” economy is arising. This new economy needs a new set of rules and values, which determine the behavior of its actors. Participants in the digital market realize that traditional attitudes and perspectives in doing business need to be redefined. In this dynamic and turbulent environment that requires flexible and fast responses to changing business needs organizations have to respond by adopting decentralized, team-based, and distributed structures variously described in the literature as virtual, networked, cluster, and resilient virtual organizations. One main aspect of this approach is that organizations in this environment are networked, that is, interlinked on various levels through the use of different networking technologies. Today, besides the Internet, new solutions are offered: wireless networks. Collaboration and cooperation are main characteristics of virtual organizations, so the contacts among the users, the human beings, have outstanding importance. A very important element of this human contact is trust. In a networked organization, trust is the atmosphere, the medium in which actors are moving (Castelfranchi & Tan, 2001). Trust is the basis of cooperation, the normal behavior of the human being in the society. The ability of enterprises to form networked systems depends on the existing level of trust in the society and on the capital of society (Fukuyama, 1995). As the rate of cooperation is increasing in all fields of life, the importance of trust is evolving even faster. In this new organizational environment new methods and techniques of trust building have to be developed, as the conventional rules cannot be applied. According to different experiments, the level of trust between cooperating virtual teams is highly influenced by the type of communication and the duration of contacts.