The possibility of a p-wave "equal-spin-pairing" superconducting state is predicted in itinerant ferromagnets. The pairing interaction is mediated by the exchange of longitudinal spin fluctuations, and the resulting state is analogous to the Al phase of superfluid He. We describe the system in terms of a Hubbard-type exchange interaction constant I and a Stoner enh incement factor S = (1 -I ) . As I is varied and the ferromagnetic transition is approached from either the ferromagnetic or paramagnetic side, the p-state transition temperature goes through a maxirnum and then falls to zero. Rough calculations of the transition temperature indicate that tnis state should be observable in very clean samples of weak itinerant ferromagnets at currently attainable temperatures.Applications to ZrZn2 and Ni are discussed.

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