Physiological motion remains a major challenge for cardiac PET-MR. Here we propose a framework for non-rigid respiratory motion-corrected simultaneous Coronary MR Angiography (CMRA) and cardiac PET. Motion estimated from low-resolution MR image navigators and from CMRA data itself is used for correcting CMRA and PET datasets to the same respiratory position. The proposed CMRA approach was validated in ten healthy subjects. Results from the PET-CMRA framework on three patients show that motion-corrected PET images have improved sharpness compared to uncorrected reconstructions, whereas motion-corrected CMRA images have improved coronary vessel length and sharpness compared to uncorrected and translational-corrected images.