An experiment was carried out to investigate whether a local breed of cattle is better adapted than European breed crosses to low quality feeds and to variations in their supply. Four Red Chittagong (RC) and four Holstein cross Sahiwal (Hx) cattle were used to compare the intake and digestibility of German grass (Echinocloa crusgalli) and rice straw with four regimes of feed supply. These were; a choice of German grass and rice straw each offered ad libitum on the same day (A); German grass and rice straw offered ad libitum on alternate days (B); rice straw offered ad libitum for 5 days followed by German grass ad libitum for 5 days (C); and German grass offered ad libitum for 5 days followed by rice straw ad libitum for 5 days (D). Each breed was offered the treatments in a 4×4 Latin Square design. The German grass intake and total dry matter intake per kg metabolic live weight were significantly higher for the Hx than for RC, but there were no significant effects of genotype on digestibility of nutrients or live weight. Treatment A had the highest proportion of German grass relative to rice straw in the total DM intake, and had the highest total DM intake and apparent digestibility of nutrients compared with treatments B, C and D. It was concluded that there was no significant evidence that the RG cattle were better adapted to a variable supply of low quality feed than Hx cattle, and that the variable feed supply reduced the ability of cattle to select a preferred diet and consequently nutrient intake was depressed.