We consider the problem of node positioning in ad hoc networks. We propose a distributed, infrastructure- free positioning algorithm that does not rely on GPS (Global Positioning System). Instead, the algorithm uses the distances between the nodes to build a relative coordinate system in which the node positions are computed in two dimensions. Despite the distance measurement errors and the motion of the nodes, the algorithm provides sufficient location information and accuracy to support basic network functions. Examples of applications where this algorithm can be used include Location Aided Routing and Geodesic Packet Forwarding. Another example are sensor networks, where mobility is less of a problem. The main contribution of this work is to define and compute relative positions of the nodes in an ad hoc network without using GPS. We further explain how the proposed approach can be applied to wide area ad hoc networks. Keywords: ad hoc, mobile, distributed, wireless networks, personal communication system, self-locating, radio-location, GPS-free, self-organization.