A new technique for discrimination between Parkinsonian tremor and essential tremor is investigated in this paper. The method is based on spectral analysis of both accelerometer and surface EMG signals with neural networks. The discrimination system consists of two parts: feature extraction part and classification (distinguishing) part. The feature extraction part uses the method of approximate spectral density estimation of the data by implementing the wavelet-based soft decision technique. In the classification part, a machine learning approach is implemented using back-propagation supervised neural network. The data has been recorded for diagnostic purposes in the Department of Neurology of the University of Kiel, Germany. Two sets of data are used. The training set, which consists of 21 essential-tremor (ET) subjects and 19 Parkinson-disease (PD) subjects, is used to obtain the important features used for distinguishing between the two subjects. The test data set, which consists of 20 ET and 20 PD subjects, is used to test the technique and evaluate its performance.