Ad hoc networks of autonomous vehicles endowed with inter-vehicular communication (IVC) capabilities are in our future. Avoidance of accidents in safety-critical (SC) scenarios is a major concern. We show that IVCs can " solve " safety-related problems that are not within the grasp of sensing/robotics. A rigorous definition of SC IVCs is given, based on the Bounded Move (BM) requirements. Longitudinal SC scenarios in ad hoc strings and lateral inter-string SC scenarios as they arise on highways are examined. Since current WAVE standards (IEEE 802.11p, ETSI ITS-G5) fail to meet the BM requirements by huge margins, novel solutions are sought. We present the cohort construct—a string with a specification, a deterministic MAC protocol that also achieves fast string-wide message dissemination, and two distributed agreement algorithms. Worst-case time bounds achieved by these solutions are given, showing that they meet the BM requirements. Anonymity issues are briefly addressed.