Artificial neural networks are brain-like structures used in mathematical modelling that excel in pattern recognition. In this research, a simple feed-forward artificial neural network, trained by error back-propagation algorithm, was used as a tool to relate peak Cryptosporidium and Giardia concentrations with other biological, chemical and physical parameters in surface water. Multiple water quality parameters at a water treatment plant intake on the Delaware River, New Jersey, USA, collected in 1996, were provided to the authors for recognition analysis. Water samples were classified as "background" and "above background" based on the concentration of full and empty oocysts and cysts of Cryptosporidium and Giardia. The results of this preliminary effort were encouraging. Parameters significant to the identification of each protozoa were identified, eight for Cryptosporidium and seven for Giardia by a stepwise elimination technique. Data withheld from the model training was used to validate the trained models and evaluate the most effective internal architecture. In both cases, the best prediction performance was found when the number of internal nodes was twice that of the input parameters in single hidden-layer architecture. Predictions for the classification of the verification data set resulted in no false-negatives (mis-prediction of above background protozoa concentrations) when the models were optimally trained.