For ECG interpretation, the detection and delineation of P and T waves are challenging tasks. This paper proposes sequential Bayesian methods for simultaneous detection, threshold-free delineation, and waveform estimation of P and T waves on a beat-to-beat basis. By contrast to state-of-the-art methods that process multiple-beat signal blocks, the proposed Bayesian methods account for beat-to-beat waveform variations by sequentially estimating the waveforms for each beat. Our methods are based on Bayesian signal models that take into account previous beats as prior information. To estimate the unknown parameters of these Bayesian models, we first propose a block Gibbs sampler that exhibits fast convergence in spite of the strong local dependencies in the ECG signal. Then, in order to take into account all the information contained in the past rather than considering only one previous beat, a sequential Monte Carlo method is presented, with a marginalized particle filter that efficiently estimates the unknown parameters of the dynamic model. Both methods are evaluated on the annotated QT database and observed to achieve significant improvements in detection rate and delineation accuracy compared to state-of-the-art methods, thus providing promising approaches for sequential P and T wave analysis.