The present invention relates to flame retardant polymer compositions possessing non-linear structural configurations. According to the invention, a preformed backbone polymer, selected from polyolefins or styrenic polymers or copolymer thereof, is reacted with a flame retardant reagent selected from tribromophenoxy- or pentabromophenoxy ethyl ester or acrylic or methacrylic acid. The non-linear structural configuration is a result from the grafting or crosslinking of the ester with the polymer. The preferred amounts of the flame retardant reagent in the polymer compositions are between 10% to 50% by weight of the compositions. The flame retardant reagents are characterized by their thermostability at high temperatures. Optionally synergistic fire retardant additives such as antimony oxide are incorporated in the compositions. The flame retardant ethylene-­propylene rubber compositions were found to possess improved properties with a V-O rating, being completely absent of any blooming effect.