We consider self-consistent spinning fluid cosmologies in bath general relativity in Riemannh spacetimes and Einstein-theory in Riemano-CW spacetimes. First we extend slightly the cosmological calculation of Marlin eral for general relativistic self-consistent spinning Buids. The existence of spin-squared terms in the field equations in the Einstein-cutan theory shows, however, that an expanded class of meaningful cosmologies is possible. Under certain assumptions on the arbikariness of the cosmological shear and expansion the results for the ad hoc Weyssenhofl spin fluid in a spherically symmehic spacetime can be reproduced.