This paper presents lossless compression schemes for ECG signals based on neural network predictors and entropy encoders. Decorrelation is achieved by nonlinear prediction in the first stage and encoding of the residues is done by using lossless entropy encoders in the second stage. Different types of lossless encoders, such as Huffman, arithmetic, and runlength encoders, are used. The performances of the proposed neural network predictor-based compression schemes are evaluated using standard distortion and compression efficiency measures. Selected records from MIT-BIH arrhythmia database are used for performance evaluation. The proposed compression schemes are compared with linear predictor-based compression schemes and it is shown that about 11% improvement in compression efficiency can be achieved for neural network predictor-based schemes with the same quality and similar setup. They are also compared with other known ECG compression methods and the experimental results show that superior performances in terms of the distortion parameters of the reconstructed signals can be achieved with the proposed schemes.