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Epilepsy is a brain disorder disease that affects people's quality of life. Electroencephalography (EEG) signals are used to diagnose epileptic seizures. This paper provides a computer-aided diagnosis system (CADS) for the automatic diagnosis of epileptic seizures in EEG signals. The proposed method consists of three steps, including preprocessing, feature extraction, and classification. In order to perform the simulations, the Bonn and Freiburg datasets are used. Firstly, we used a band-pass filter with 0.5–40 Hz cut-off frequency for removal artifacts of the EEG datasets. Tunable-Q Wavelet Transform (TQWT) is used for EEG signal decomposition. In the second step, various linear and nonlinear features are extracted from TQWT sub-bands. In this step, various statistical, frequency, and nonlinear features are extracted from the sub-bands. The nonlinear features used are based on fractal dimensions (FDs) and entropy theories. In the classification step, different approaches based on conventional machine learning (ML) and deep learning (DL) are discussed. In this step, a CNN–RNN-based DL method with the number of layers proposed is applied. The extracted features have been fed to the input of the proposed CNN–RNN model, and satisfactory results have been reported. In the classification step, the K-fold cross-validation with k = 10 is employed to demonstrate the effectiveness of the proposed CNN–RNN classification procedure. The results revealed that the proposed CNN–RNN method for Bonn and Freiburg datasets achieved an accuracy of 99.71% and 99.13%, respectively. [ABSTRACT FROM AUTHOR]