Spatially resolved small-angle neutron scattering, SANS, has been used to investigate the response of the mixed microstructure of the dialkyl chain cationic and nonionic surfactant mixtures of (2,3-diheptadecyl ester ethoxy-n-propyl-1), 1,1,1-trimethyl ammonium chloride/octadecyl monododecyl ether, DHTAC/C18EO10, and DHTAC/dodecyl monododecadecyl ether, Coco20, over the velocity flow pattern of a crossed-slot elongational flow cell. The two different surfactant mixtures have different relative amounts of lamellar and micellar components, and this results in some differences in the flow-induced response. For the DHTAC/C18EO10, which is predominantly in the form of lamellar fragments, a complex pattern of orientational ordering is observed which reflects the competition between or demixing of the two principal flow directions in the cell.