Dual-skinned hollow fiber membranes were produced with thin skins on both the inner (lumenal) and outer surfaces of an annular macroporous matrix. These dual-skinned membranes demonstrated a clear directional selectivity with sieving coefficients that were dramatically different in the two flow directions (shell-to-lumen and lumen-to-shell). Unlike the incidental directional selectivity previously reported with single-skinned reverse osmosis membranes, sieving coefficients in both directions are controllable by varying the properties of the two skin layers. The directional sieving behavior of these membranes is a result of the directional nature of the convective solute transport across a membrane having two skin layers with different effective pore sizes. Internal concentration polarization significantly increases solute sieving coefficients when flow occurs through the more open skin layer first, but is largely absent when the flow is in the other direction. The internal concentration polarization also has a strong effect on the solvent flux through these membranes causing large directional differences in flux during filtration of a dilute macromolecular solution. The unique transport characteristics of these dual-skinned membranes thus provide an extraordinarily powerful tool for the design and development of novel membrane devices and processes that exploit the directional selectivity of these new membrane structures.