Disclosed is a process for preparing substantially non-crosslinked ethylene methylacrylate copolymers grafted with a grafting agent such as maleic anhydride. In particular, in the process of the present invention, it has been found that the use of very small amounts, i.e., less than about 0.2 weight percent, of a free-radical initiator in combination with the grafting agent and the ethylene methylacrylate copolymer, but in the absence of solvent, results in a grafted product having little or no crosslinked component. The grafted copolymers have utility in food packaging.