Abstract. Let V be a Zariski-open (i.e., cofinite) subset of an infinite field K. Call a map m: V x V-*V separately polynomial if for each x e V the two partial mapsy -> m(x,y), y -» m(y, x) are polynomial. Ifm: V X P"-» K is a separately polynomial group law, then either V = K and m(x, y) = x + y + k for some ks. KotV = K-{k}aaà m(x,y) = b(x -k)(y -k) + k for some k e K and