Effective permeability KP, the ultrafiltration coefficient (KUF), the sieving coefficient (SC), and the loss/permeation of proteins (primarily albumin) are key parameters/specifications characterizing hemofilter (HF) performance. However, there are uncertainties regarding their determination. This work aims (a) to demonstrate that the co-current flow (of blood and dialysate) can lead to beneficial unidirectional filtration (from blood/plasma to dialysate) under a fairly uniform local trans-membrane pressure (TMP), unlike the presently employed counter-current flow; (b) to study the temporal evolution of key HF performance parameters under co-current flow, particularly during the important early stage of hemocatharsis (HC). Experiments with human plasma and BSA solutions in co-current flow mode (for which a fluid mechanical model is developed) show a fairly uniform local/axial TMP, which also improves the local/axial uniformity of protein membrane fouling, particularly under (currently favored) high convective flux operation. Due to incipient membrane fouling, a significant temporal variability/decline in the effective KP is observed, and, in turn, of other parameters (i.e., the Kuf, SC, and permeation/mass flux Mm for albumin and total proteins). A satisfactory correlation of the albumin/protein mass flux Mm with permeability KP is obtained, indicating strong inter-dependence. In conclusion, co-current flow, allowing for a fair local TMP axial uniformity, enables the acquisition of accurate/representative data on the evolution of HF parameters, facilitating their interpretation and correlation. The new results provide a basis for exploring the clinical application of the co-current flow.