In the present work an Artificial Neural Network (ANN) and a Probabilistic Neural Network (PNN) were used in detecting EEG sleep spindles. The networks were trained separately using the same spindles. The networks were trained separately using the same spindles. False positives (FPs) were characterized in two categories: FP1 included FP indications by the system, when no spindles were visually detected and FP2 concerned the case when a visually detected spindle corresponded to two distinct spindle indications by the system. ANN had higher sensitivity than PNN, when the classifiers functioned separately (88.5% vs 75.8%). All spindles detected by PNN were also detected by ANN. If only FP1s were taken into account, then FP rate was 16.6% and 0% respectively. The combination of a two-stage detector, with the first level being the ANN and the second being the PNN resulted in a system retaining the sensitivity of the ANN, and the ability to characterize the spindles indicated by the system into two categories, those indicated by both networks, with a probability of 3.5% to be FPs, and the remaining ones, which need a second round of visual inspection, because they have a high probability (56.7%) to be FP indications.