The structural organization of the concentration polarization layer (CPL) during the cross-flow membrane separation process of anisometric aqueous suspensions of colloidal cellulose nanocrystals and beidellite clay particles has been characterized by in situ time-resolved small-angle X-ray scattering (SAXS). Dedicated cross-flow filtration cells were implemented on the ID02 TRUSAXS beamline at the European Synchrotron Radiation Facility (Grenoble, France). From the analysis of the scattered intensities and structure factors of particles in the CPL, both the concentration profiles ɸ(Δz,Δt) and anisotropic structural organization have been characterized as a function of filtration time (Δt) and distance from the membrane surface (Δz). Remarkably, a coupling between concentration and anisotropy was revealed and modeled using either a simple or stretched exponential trend for rod- or disk-like systems, respectively. Using a simple filtration model, the time evolution of the deposit thickness, membrane resistance and specific resistance of the deposit, deduced from an analysis of the normalized concentration profiles, allowed directly predicting the rapid decay of permeate flux associated to the exponential growth of concentration and anisotropic organization inside the CPL. Ex situ scanning electron microscopy (SEM) observations and wide-angle X-ray diffraction (WAXD) analyses performed on dried deposits parallel and perpendicular to the membrane surface revealed well-defined layered structures from nanometer to micrometer length scales.