Reaction products of polymeric alkyl phenol formaldehyde resins are useful as additives to inhibit or prevent the deposition or precipitation of asphaltenes in hydrocarbon fluids, particularly crude oil produced from a subterranean formation. These reaction products are formed by reacting a polymeric alkyl phenol formaldehyde resin with a co-reactant having functional groups including, but not necessarily limited to, amines, esters, silanes, ketones, epoxides, alkoxides, aryloxides, halogens, alkali metals, alkali earth metals, acetamides, non-metal oxides, metal oxides, where the co-reactant optionally has a carbon chain length between 1 and 22 and the reaction is conducted in the presence of at least one of various solvents. In one non-limiting embodiment, the co-reactant is a silicon derivative. The asphaltene inhibitors have utility when injected into a subterranean formation while oil production temporarily halts, a process called “squeezing,” because they are retained to a degree in the formation as the crude oil is produced.