Abstract: Method for killing a cycling cell, by contacting the cell with a first agent that blocks progression of the cell cycle in the cell, and thereafter contacting the cell with a second agent that overrides the cell cycle block such that the cell proceeds past mitosis and cell death results within an additional cell cycle due to aberrant DNA replication or chromosome segregation. The first agent blocks the progression of the G.sub.1, S, G.sub.2, or mitosis stage of the cell cycle. The second agent is preferably 2-aminopurine (2-AP) or 6-dimethylaminopurine (6-DMAP). The duration of contact with the first agent is advantageously limited to a first time period sufficient to block the progression of the cell cycle, and the duration of contact with the second agent is limited to a second time period sufficient to override the cell cycle block.