The invention relates to a low-lactose and a lactose-free milk product and to a process for the production thereof. The lactose in the milk raw material is hydrolyzed, proteins, minerals and sugars are separated into different fractions by the membrane technique, and a low-lactose or a lactose-free milk product is composed from the fractions. The invention provides a milk product, the water therein originating from the original milk raw material. In addition, useful by-products are produced in the process.