Essential tremor (ET) and the tremor in Parkinson's disease (PD) are the two most common pathological tremors with a certain overlap in the clinical presentation. The main purpose of this work is to use an artificial neural network to select the best features and to discriminate between the two types of tremors. The features used are of hybrid type obtained from two different algorithms: the statistical signal characterization (SSC) of the signal describing its morphology, and the soft-decision wavelet-decomposition (SDWD) features extracted from the accelerometer and surface EMG signals. The SSC method is used to obtain morphology-based features of the spectrum of the accelerometer and two surface EMG signals. The SDWD technique is used in this work to obtain the approximate spectral representation of both accelerometer and the two surface EMG signals. Two sets of data (training and test) are used in this paper. The training set consists of 21 ET subjects and 19 PD subjects, while the test set consists of 20 ET and 20 PD subjects. A neural network of the type feed forward back propagation has been used to combine best SSC features and best SDWD features of the accelerometer and EMG signals. Efficiency result of 92.5% was obtained using best hybrid features. The artificial neural network has been used successfully to combine two types of features in an automatic discrimination system between PD and ET.