NOVELTY - Stabilizing (M1) asphaltenes in petroleum feedstock, comprises adding at least one additive to the feedstock containing asphaltenes to improve stability of asphaltenes in petroleum feedstock. The additive comprises: at least one biological source oil e.g. algae oils and/or vegetable oils; and/or at least one chemical additive including alkyl-phenol based resins or their derivatives, long chain alpha -olefins having more than 20C reacted with an aldehyde, long chain alkyl phenate sulfides having 8-40C reacted with polyolefins, and/or metal oxide-based colloidal hydrocarbon-based nanodispersions.    USE - The methods are useful for stabilizing asphaltenes in a petroleum feedstock.    ADVANTAGE - The method: stabilizes the asphaltenes in the petroleum feedstock to an extent that is greater than the stabilization achieved with addition of only the same amount of the biological source oil separately, or the stabilization achieved with addition of only the same amount of the chemical additive separately (claimed), hence provides synergistic effect in stabilizing asphaltenes, and avoids or prevents problematic issues caused by the asphaltenes, including sludges, plugging, deposits, fouling and/or corrosion in the production, transferring and processing of the petroleum feedstocks; can be performed in an economical manner; and improves the quality and stability of the feedstock.    DETAILED DESCRIPTION - Stabilizing (M1) asphaltenes in a petroleum feedstock, comprises adding at least one additive to the petroleum feedstock containing asphaltenes to improve the stability of asphaltenes in the petroleum feedstock. The additive comprises: at least one biological source oil including algae oils, vegetable oils, fish oils, animal oils, cooking oils, biomass derived oils, bio-crude and/or synthetically-produced oils; and/or at least one chemical additive including alkyl-phenol based resins or their derivatives (where the alkyl group is octyl, nonyl or dodecyl, an alkyl-phenol is reacted with an aldehyde in the presence of a sulfonic acid, and the alkyl-phenol based resins are used alone or in conjunction with amines), long chain alpha -olefins having more than 20C reacted with an aldehyde, long chain alkyl phenate sulfides having 8-40C reacted with polyolefins, and/or metal oxide-based colloidal hydrocarbon-based nanodispersions. An INDEPENDENT CLAIM is also included for stabilizing (M2) asphaltenes in the petroleum feedstock, comprising: evaluating the petroleum feedstock for asphaltene stability; preparing many blends, when the petroleum feedstock exhibits asphaltene instability, where each blend has a different proportion ratio of the petroleum feedstock to the biological source oil and/or the chemical additive, and the biological source oil and/or the chemical additive is the same in each blend; and evaluating each blend for asphaltene stability by selecting the blend that best improves the asphaltene stability of the petroleum feedstock in the blend.