Process for manufacturing cheeses and other dairy products, and the resulting products, in which lactobionic acid is added, or generated in situ, in combination with a dairy component in the course of the process. The lactobionic acid can be used as the sole acidulent for direct acidification of the cheese, or in conjunction with reduced amounts of lactic acid culture. When the lactobionic acid is generated in situ during cheese manufacture according to the invention, a lactose oxidase is used in one embodiment to convert lactose intrinsically present in the dairy liquid ingredient(s) into lactobionic acid. The organoleptic attributes of the cheeses made using lactobionic acid as an ingredient are satisfactory and fully suitable. The process can be applied to the production of a wide variety of cheeses, including, for example, cream cheeses, hard cheeses such as cheddar, UF cheeses, process cheeses, cheddar cheeses, and so forth.