This paper is devoted to the study of best approximation estimates for generalized Liouville–Weyl derivatives using angular approximation of functions in a multidimensional space. We consider generalized Liouville–Weyl derivatives, which are used instead of classical mixed Weyl derivatives. The concept of general monotone sequences plays an important role in the study. The paper consists of three sections. The first section contains basic definitions and a brief historical overview. The second section presents known statements necessary for proving the key results. In the third section, upper estimates for the best angular approximations of functions of several variables are obtained. The topic considered in this paper is related to the issues studied in the works of A.A. Konyushkov, Stechkin, Timan, M.K. Potapov, B. Simonov, S. Tikhonov.