Marine fuel oil stability has always been an issue for bunkering companies and ship owners all around the world and the problem has become even more apparent with the introduction of the Global Sulphur Gap by the International Maritime Organization (IMO) in 2020. In this article, the historical background and the technical reasons why marine fuel oils lose their stability, as well as methods for preventing such instability from occurring, are presented. While it is possible to make fuel compositions stable by adjusting their composition in such a way that the components of the fuel are compatible, considering that marine fuel oils are often comprised of the least value-added products, the method of adding special fuel oil stabilizers (also known as “asphaltene dispersants”) is usually preferred. An overview of such stabilizers is presented; their chemical composition, based on the information provided by the manufacturers and/or inventors is studied. In addition, the experimental research of the produced marine fuel oil and its components is carried out. The results of the model composition studies show that adding even as little as 10% of residual asphaltene-rich components can make a composition with a high stability reserve unstable. It was also shown that the content of the asphaltene-rich component in a stable fuel can be increased from 3% to 10% by introducing stabilizers in low amounts (up to 2000 ppm), thus lowering the amount of higher value-added, mostly naphthene-paraffinic-based components. Different methods of fuel stability evaluation were studied and tested, most of them being in correlation with one another. Several types of stability enhancers were tried out on unstable fuel, with stabilizers based on alkylphenol formaldehyde resin showing the best results.