A general theorem on absolute Norlund sum- mability factors of infinite series has been obtained. The theorem includes, as special cases, a number of well-known results. Several new results can also be deduced from it. 1. Let />n = 0, qn>0, Qn=qa+qi + - ' -+qn-+co, Pn=p0+Pl + - ■ -+pn and P_1=/7_1 = o-i=0. Let 2 an he a given infinite series with sn as its «th partial sum. The series 2 an 's sa'd to be summable \N,p | if tneBV, where tn=Pn1 2*=o/>n-*J*> F^0. It is said to be summable \N, qn if TneBV, where Tn = Q^ 2*=o qA- It is well known that necessary and sufficient conditions for the method (N,pn) to be absolutely regular are: