The Traffic Alert and Collision Avoidance System (TCAS) has been developed to reduce mid air collisions between transponder equipped aircraft. The TCAS concept encompasses a range of capabilities. TCAS I is a low-cost version which provides traffic advisories only. TCAS II adds vertical resolution advisories and is intended to provide a comprehensive level of separation assurance in all current and predicted airspace environments through the end of this century. Enhanced TCAS II uses more accurate intruder bearing data to allow it to generate horizontal resolution advisories. All three forms of TCAS equipment track aircraft equipped with both the existing Air Traffic Control Radar Beacon System (ATCRBS) transponders and with the new Mode S transponders. A TCAS equipped aircraft makes ATCRBS or Mode S range measurements on nearby aircraft. The ATCRBS or Mode S replies contain the altitude of the aircraft if it has an encoding altimeter. TCAS II uses range rate and altitude rate to decide if a collision is imminent. Therefore the replies from a given aircraft must be tracked and correlated in range and altitude. This report documents surveillance techniques developed by Lincoln Laboratory for use by TCAS II equipment in tracking aircraft equipped with ATCRBS transponders. Specifically, it describes the two tracking algorithms used for ATCRBS replies. One algorithm is for aircraft that report altitude, and the other is for those that do not.