Respiratory motion causes artifacts and blurring of cardiac structures in reconstructed images of SPECT and PET cardiac studies. Hysteresis in respiratory motion causes the organs to move in distinct paths during inspiration and expiration. Current respiratory motion correction methods use a signal generated by tracking the motion of the abdomen during respiration to bin list- mode data as a function of the magnitude of this respiratory signal. They thereby fail to account for hysteretic motion. The goal of this research was to demonstrate the effects of hysteretic respiratory motion and the importance of its correction for different medical imaging techniques particularly SPECT and PET. This study describes a novel approach for detecting and correcting hysteresis in clinical SPECT and PET studies. From the combined use of MRI and a synchronized Visual Tracking System (VTS) in volunteers we developed hysteretic modeling using the Bouc-Wen model with inputs from measurements of both chest and abdomen respiratory motion. With the MRI determined heart motion as the truth in the volunteer studies we determined the Bouc Wen model could match the behavior over a range of hysteretic cycles. The proposed approach was validated through phantom simulations and applied to clinical SPECT studies.