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It is shown that unlike the perfect fluid case, anisotropic fluids (principalstresses unequal) may be geodesic, without this implying the vanishing of(spatial) pressure gradients. Then the condition of vanishing four accelerationis integrated in non-comoving coordinates. The resulting models are necessarilydynamic, and the mass function is expressed in terms of the fluid velocity asmeasured by a locally Minkowskian observer. An explicit example is worked out.Comment: 13 pages Latex, three ps. figures, to appear in J. Math. Physic

Anisotropic geodesic fluid spheres in general relativity