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The aim of this paper is to prove the following theorem concerning the term by term differentiation the-orem of Walsh-Kaczmarz series. Let (ck ) be a decreasing real sequence with ck＝o( 1/(logk)r )γ ) for some γ＞ 1.Theng(x) ＝∞∑k=1ckκk(x), f(x) ＝∞∑k=1 ck/k