This invention pertains to the use of compounds containing amide or imide type functional groups to increase the rate of nitroxide mediated oxidation of alcohols, particularly primary and secondary alcohols. While suitable for oxidation of alcohol groups on a variety of substrates, it is particularly useful to oxidize cellulose, cellulose pulp or cellulose fiber such that it is commercially compatible with the traditional paper making process. Such co-catalysts may be used to increase the absolute amount of aldehyde groups on cellulose, cellulose pulp or cellulose fiber, thereby further increasing the inherent wet strength, temporary wet strength, and dry strength of paper made with such cellulose, cellulose pulp or cellulose fiber.