The study is devoted to establishing the nature of the distribution of domain-specific and domain-unspecific cognitive resources in the working memory system. Data on the effectiveness of tasks requiring activation of domain-specific components of working memory with different types of cognitive load were used. The subjects (N=32) performed tasks to measure the amount of working memory, requiring simultaneous execution of two tasks: the main and the interfering (dual task). The task "Volume of symmetry", aimed at activating the visual-spatial component of working memory, and "Volume of reading letters", aimed at activating the verbal component of working memory, were used as double tasks. In the "Volume of symmetry" problem, it was necessary to reproduce the location of points in 3x3 matrices in the correct sequence (the main task) and determine the symmetry of the location of points in 9x9 matrices (the interfering task). In the task "The volume of reading letters", it was necessary to reproduce the numbers in the correct sequence (the main task) and determine whether the letter is a vowel or a consonant (an interfering task). The above tasks were performed under conditions of visual-spatial cognitive load (tapping) and verbal cognitive load (speaking), aimed at attracting cognitive resources to provide components of working memory of the corresponding modalities. The presented data are considered within the framework of a concentric model that assumes the presence of a focus of attention, a region of direct access and activated long-term memory in the working memory. The results obtained support the presence in the working memory system of modal-nonspecific cognitive resources contained in the direct access region (up to four elements), and confirm the presence of modal-specific cognitive resources in case of exceeding the optimal number of elements in the direct access region (more than four elements). A greater susceptibility of the verbal component of working memory to cognitive load compared to the visual-spatial one was also demonstrated. The obtained results are compared with the data of previous studies of the functional organization of working memory, the composition of its components and their interaction in solving cognitive tasks.