In 1984, \textit{M. Hata} and \textit{M. Yamaguti} [Japan J. Appl. Math. 1, 183-199 (1984; Zbl 0604.26004)] examined the Takagi function (the function \(T(x) =\sum 2^{-n} \psi(2^n x)\), where \(\psi (x) =1 -|2x -2[x] -1|\), which is a well-known example of a nowhere differentiable continuous function), as well as its generalization \(\sum a_n \psi(2^{n-1} x)\) (where \(\{a_n\} \in l_1\)), called a Takagi series. The graphs of such functions may be fractal sets. While some upper bounds of the Hausdorff dimension of their graphs are known, the exact Hausdorff dimension has been obtained in only a few cases [\textit{A. S. Besicovitch} and \textit{H. D. Ursell}, J. London Math. Soc. 12, 18-25 (1937; Zbl 0016.01703)]. In the paper under review the author generalizes the notion of a Takagi series replacing the function \(\psi\) by any function \(\varphi\) fulfilling a few natural conditions. It is shown that the upper box-counting dimension of the graph of a generalized Takagi series equals \(\max \bigl\{2 +\overline{\lim}_n \log_2 |a_n|^{1/n}, 1\bigr\}\), so it depends only on the coefficients \(\{a_n\}\) but not on \(\varphi\). The author studies also the lower box-counting dimension of such graphs, providing its estimate or, in several cases, its exact value.