Fuel oils, especially heavy fuel oils that are subject to instability on storage can be treated with additives in order to stabilizer the fuel oil in regard to precipitating contaminants such as asphaltenes. Alkylphenol resins, either with or without components selected from the group consisting of a fatty acid amides, mannich resins and mixtures thereof are effective additives for stabilizing fuel oils. It is emphasized that this abstract is provided to comply with the rules requiring an abstract which will allow a searcher or other reader to quickly ascertain the subject matter of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims. 37 CFR 1.72(b)