To provide a method of suppressing the formation of coke on a heat transfer surface to be used for cooling or heating a petroleum feedstock under the coke formation conditions.

In order to inhibit the formation of coke on a heat transfer surface, the heat transfer surface is treated with an effective amount of a specific phosphonate. This phosphonate does not contribute to any corrosion and does not form any hazardous by-product. This phosphonate is represented by the formula: (R'Y)2P(X)R" (X and Y are O or S; R' is an alkyl or a substitutent bearing hetero atoms that do not directly bond to the phosphorus atoms and has 4-20 carbon atoms; R" is an alkyl or a substituent-bearing hetero atoms that do not directly bond to the phosphorus atoms and has 6-30 carbon atoms).