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In this paper we study $ L^1 $-convergence of the $ r $-th derivatives of Fourier series with complex-valued coefficients. Namely new necessary-sufficient conditions for $L^1$-convergence of the $ r $-th derivatives of Fourier series are given. These results generalize corresponding theorems proved by several authors (see [7], [10], [13], [19]). Applying the Wang-Telyakovskii class $ ({f B}{f V})_r^sigma $, $ >sigma>0 $, $ >r=0,1,2,ldots, $ we generalize also the theorem proved by Garrett, Rees and Stanojevi'{c} in [5]. Finally, for $ sigma=1 $ some corollaries of this theorem are given

Generalization on some theorems of $ L^1 $-convergence of certain trigonometric series