A new mode of transport is described that was capable of high-resolution separation of superparamagnetic materials from complex mixtures based on their size. Laminar flow and a rotating external magnetic field were applied to superparamagnetic beads assembled on a semiperiodic micromagnet array. Beads at the edge of the micromagnet array oscillated in-phase with the external magnetic field with an amplitude that decreased with increasing frequency, omega, until they reached an immobilization frequency, omega(nu) where the beads stopped moving. Laminar flow along the edge of the array could be tuned to sweep the beads for which omega < omega(i) downstream at a velocity that increased with size while leaving beads for which omega > omega(i) undisturbed. Flow-enhanced nonlinear magnetophoresis (F-NLM) promises to enable multiple superparamagnetc bead types to be used in the fractionation of cells and implementation of diagnostic assays.