Flux declines versus time (t) during crossflow microfiltration of a mixture that contains phosphate and fly ash, were modeled and compared by using an artificial neural network (ANN) and Koltuniewicz's method (KM) at different conditions of fly ash dosages (C-FA), PO4 concentrations (C-PO4), transmembrane pressures (DeltaP) and two membrane types (M-T). Two different neural network (NN) architectures (NN1, NN2) that gave the best prediction of flux values were established for data analyses. KM was also taken as Kl and K2 to compare the predictions of both models at the same experiments separately. It was shown that all of the experimental conditions can be modeled as a whole or separately, and the model results obtained for one experiment can be used for others at the same conditions with an acceptable correlation level by NNs while not with Koltuniewicz. The correlation values were found as 0.991 and 0.988 for NN1 and NN2, and 0.972 and 0.973 for Kl and K2, respectively. These results are put forward to show that ANN results fit better to fluxes than KM according to correlation values (r(2)). The normalized flux values obtained from K1 and K2, smaller than 0.4, are in the range between -30 and 40% variations, whereas the most of N1 and N2 variations are in the range of +/-20%. The error distributions of data used for NN1 and NN2 were found to be 82 and 79%, while for K1 and K2 was calculated to be 51 and 52%, in the range of +/-10% error, respectively. The contribution of t variable to flux values provided by NNs was determined in an important level at the range of 40-50% due to increasing in membrane fouling by the time. The contributions of DeltaP, C-FA and C-PO4 variables were found in the range of 15-25%. The affect of MT was determined at a lower level about for 4%. As a conclusion, using elaborated ANN modeling, it is able to predict the permeate flux at a high accuracy from process variables such as transmembrane pressure, various concentrations of feed solution and membrane type and contributions of process variables to the permeate flux value. (C) 2004 Elsevier B.V. All rights reserved.