Objective: To develop a method for detection of bradycardia and ventricular tachycardia using the photoplethysmogram (PPG). Approach: The detector is based on a dual-branch convolutional neural network (CNN), whose input is the scalograms of the continuous wavelet transform computed in 5-s segments. Training and validation of the CNN is accomplished using simulated PPG signals generated from RR interval series extracted from public ECG databases. Manually annotated real PPG signals from the PhysioNet/CinC 2015 Challenge Database are used for performance evaluation. The performance is compared to that of a pulse-based reference detector. Results: The sensitivity/specificity were found to be 98.1%/97.9 and 76.6%/96.8% for the CNN-based detector, respectively, whereas the corresponding results for the pulse-based detector were 94.7%/99.8 and 67.1%/93.8%, respectively. Significance: The proposed detector may be useful for continuous, long-term monitoring of bradycardia and tachycardia using wearable devices, e.g., wrist-worn devices, especially in situations where sensitivity is favored over specificity. The study demonstrates that simulated PPG signals are suitable for training and validation of a CNN.