Summary: By using an almost increasing sequence a general theorem on \(\varphi\)-\(|C,\alpha|_k\) summability factors, which generalizes a result of H. Bor [J. Anal. 5, 33-42 (1997; Zbl 0918.40002)] on \(|C,\alpha; \delta|_k\) summability factors, has been proved under weaker conditions.