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.Then g(x) ＝∞∑k=1ckκk(x), f(x) ＝∞∑k=1 ck/k kk(x) are integrable functions and f(x) is a.e. dyadic (or Butzer and Wagner) differentiable with f[1](x) ＝ g(x) for a.e. x∈ [0,1). The function κk means the kth Walsh-Kaczmarz function.
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