Ad hoc groups, such as peer-to-peer (P2P) systems and mobile ad hoc networks (MANETs) represent recent technological advancements. They support low-cost, scalable and fault-tolerant computing and communication. Since such groups do not require any pre-deployed infrastructure or any trusted centralized authority they have many valuable applications in military and commercial as well as in emergency and rescue operations. However, due to lack of centralized control, ad hoc groups are inherently insecure and vulnerable to attacks from both within and outside the group.Decentralized access control is the fundamental security service for ad hoc groups. It is needed not only to prevent unauthorized nodes from becoming members but also to bootstrap other security services such as key management and secure routing. In this paper, we construct several distributed access control mechanisms for ad hoc groups. We investigate, in particular, the applicability and the utility of threshold cryptography (more specifically, various flavors of existing threshold signatures) towards this goal.