A summation method B is said to be stronger than a method A if the set of ,4-summable sequences is contained in the set of Bsummable sequences. The purpose of this paper is to study inclusion relations between methods for other sets of sequences. In the first section we shall introduce the notation. In the second we prove the two main theorems, and present some applications in the third part. Finally we shall mention possible generalizations and corresponding theorems for absolute summability.