A rotary bidirectional dynamic shaft seal (10) for maintaining a seal about a rotating shaft (12) to prevent the leakage of oil from the oil side of the seal past a sealing edge (18) to the air side. The seal (10) includes a plurality of pumping projections extending from the frustoconical surface (22) on the air side of the seal for pumping oil, which may leak past the sealing edge (18) back to the oil side of the seal. The pumping projection has a primary pumping surface (24) extending axially from the sealing edge (18) and a secondary pumping surface (28) extending at a shadow angle (A) away from the primary pumping (24) surface to a return surface (26) which extends generally radially to define the rear extremity of the pumping projection. Under normal operating conditions, the primary pumping surface (24) will return oil to the oil side of the sealing edge (18). However, should the shaft (12) be misaligned or be running eccentrically, the primary pumping surface (24) will engage the shaft on the minimum contact side whereas on the maximum contact side 180 degrees away, both the primary (24) and secondary (28) pumping surfaces will engage the shaft (12) to pump oil back to the oil side of the sealing edge (18).