Graft copolymers of carboxymethyl cellulose and starch with polyacrylamide have been synthesized by grafting acrylamide onto carboxymethyl cellulose and starch, respectively, using a ceric-ion-initiated solution polymerization technique. These graft copolymers have been tested for their drag-reduction effectiveness, shear stability, and biodegradability. It has been shown that grafting enhances the drag-reduction effectiveness and shear stability and also that these factors are very much dependent on the length and number of grafts in the molecule. None of the graft copolymer solutions shows any microbial degradation up to 10 days.