The T and P waves of electrocardiogram signals are excellent indicators in the analysis and interpretation of cardiac arrhythmia. As such, the need to address and develop an accurate delineation technique for the detection of these waves is necessary. In this paper, we present a novel robust and adaptive T and P wave delineation method for real-time analysis and nonstandard ECG morphologies. The proposed method is based on ECG signal filtering, value estimation of different fiducial points, applying backward and forward search windows as well as adaptive thresholds. Simulations and evaluations prove the accuracy of the proposed technique in comparison to those proposed techniques in the literature. The mean error for the T peak, T offset, P peak and P offset values are found to be 9.8, 2.3, 7.3 and 3.5 milliseconds, respectively, based on the Physionet QT database, rendering our algorithm as an excellent candidate for ECG signal analysis.