ABSTRACT: The Apollo 11 mission succeeded in landing on the moon despite two computer-related problems that affected the Lunar Module during the powered descent. An uncorrected problem in the rendezvous radar interface stole approximately 13% of the computer's duty cycle, resulting in five program alarms and software restarts. In a less well-known problem, caused by erroneous data, the thrust of the LM's descent engine fluctuated wildly because the throttle control algorithm was only marginally stable. The explanation of these problems provides an opportunity to describe the operating system of the Apollo flight computers and the lunar landing guidance software.