Ligand binding by proteins is among the most fundamental processes in nature. Among these processes the binding of small gas molecules, such as O2 , CO and NO to heme proteins has traditionally received vivid interest, which was further boosted by their recently recognized significant role in gas sensing in the body. At the heart of the binding of these ligands to the heme group is the spinforbidden reaction between high-spin iron(II) and the ligand yielding a low-spin adduct. We use computational means to address the complete mechanism of CO and NO binding by myoglobin. Considering that it involves several steps occurring on different time scales, molecular dynamics simulations were performed to address the diffusion of the ligand through the enzyme, and DFT calculations in combination with statistical rate calculation to investigate the spin-forbidden reaction. The calculations yielded rate constants in qualitative agreement with experiments and revealed that the bottleneck of NO and CO binding is different; for NO, diffusion was found to be rate-limiting, whereas for CO, the spin-forbidden step is the slowest.