In this paper, the S theta ( increment ) and N theta ( increment ) summabilities are used along with the notion of weakly unconditionally Cauchy series (in brief wuC series) to characterize a Banach space. We examine these two kinds of summabilities which are regular methods and we recall some features. Furthermore, we investigate the spaces SN theta (Ep increment wp) and SS theta (Ep increment wp) which will be thought to characterize the completeness of a space.