Exploiting differential game theories, the rules for optimal firepower assignment in a fight of single-kind arms (X-forces) versus multi-kind arms (Y-forces) are studied in this paper. It is pointed out that at each stage of the fight X-forces should concentrate al1 the remaining fire-power，to attack the kind of arms of the enemy with the maximal lighting strength, which is the product of the power coefficients of both k-forces on the kind of arms of Y-forces and the latter on the former. The similar problem in a fight of multi-kind arms versus multi-kind arms, which is more important and in which much more diffioulty is, will be discussed in another paper later.