Sleep spindles are a hallmark of the stage 2 sleep. Their distribution over the non-REM sleep is clinically important. In this paper, a method that detects the sleep spindles in sleep EEG is proposed. Short time Fourier Transform is used for feature extraction. Both multilayer perceptron and Support Vector Machine are utilized in detection of the spindles in sleep EEG for comparison. The classification performance of MLP is found to be 88.7% and that of SVM as 95.4%. It should be noted that there might be differences also in visual scoring by experts, so the results obtained are quite satisfactory.