By analytical theory and computer simulation the expected evolutionary dynamics of P transposable element spread in an infinite population are investigated. The analysis is based on the assumption that, unlike transposable elements which move via RNA intermediates, the harmful effects of P elements arise primarily in the act of transposition, and that this causes their evolutionary dynamics to be unusual. It is suggested that a situation of transposition-selection balance will be superceded by the buildup of a cytoplasmically inherited repression or by the elimination of active transposase-encoding elements from the chromosomes, a process which may be accompanied by the evolution of elements which encode proteins which repress transposition.