Close conjunction detection is the task of finding which satellites will come within a given distance of other satellites. The algorithms described here are implemented on the Connection Machine (CM) in a program called CM-COMBO. It will find close conjunctions of satellites over a time range for one, a few, or all satellites against the original or another catalog and works with an arbitrary propagator. The problem of comparing an entire catalog against itself is beyond the computing power of current serial machines. This program does not prefilter any orbits and does not make assumptions about the type of orbit (that it be nearly circular, for instance). This paper describes the algorithm for this computation, the implementation on the CM, and resuls of several studies using this program.