The results of a study to identify potential hazards arising from nuclear reactor power systems for use on the lunar and Martian surfaces, related safety issues, and resolutions of such issues by system design changes, operating procedures, and other means are presented. All safety aspects of nuclear reactor power systems from prelaunch ground handling to eventual disposal were examined consistent with the level of detail for SP-100 reactor design at the 1988 System Design Review and for launch vehicle and space transport vehicle designs and mission descriptions as defined in the 90-day Space Exploration Initiative (SEI) study. Information from previous aerospace nuclear safety studies was used where appropriate. Safety requirements for the SP-100 space nuclear reactor system were compiled. Mission profiles were defined with emphasis on activities after low earth orbit insertion. Accident scenarios were then qualitatively defined for each mission phase. Safety issues were identified for all mission phases with the aid of simplified event trees. Safety issue resolution approaches of the SP-100 program were compiled. Resolution approaches for those safety issues not covered by the SP-100 program were identified. Additionally, the resolution approaches of the SP-100 program were examined in light of the moon and Mars missions.