Four multiparous Danish Holstein Friesian cows fitted with rumen, duodenal and ileal cannulas were used in a 4 x 4 Latin square design. Treatments were arranged in a 2 x 2 factorial design to study the effect of different concentrate supplements on the intestinal digestibility of dry matter and nitrogen of artificially dried hay and rapeseed cake, estimated by the mobile bag method. Both original feeds and undegraded residues were examined. The cows were fed artificially dried hay ad libitum and one of four concentrate diets. The four concentrate diets represented two levels and two types of concentrate, where types were either dried sugar beet pulp or barley. High and low levels of concentrate were 6 and 1.5 kg/day, respectively. The type of the concentrates had no effect (P>0.05) on the total daily dry matter intake. Mobile bag N digestibility was generally not influenced by the ration fed to the cows. However, for undegraded residues of rapeseed cake a numerically small, but statistically significant higher mobile bag digestibility was found for dried sugar beet pulp compared to barley. For mobile bag dry matter digestibility the effects of ration were significant for both original and undegraded rapeseed cake whereas no effect was found for hay.