Abstract: To measure the fault diagnosis capability of the multiprocessor system with alternating group graphs as topological structures under a hybrid faulty circumstance, this paper investigates the h-restricted vertex diagnosability and the r-restricted edge diagnosability of the alternating group graphs under the HPMC model. The relationship between the two kinds of hybrid fault diagnosability is obtained by their properties. Considering that the adjacent vertices in the alternating group graphs have common adjacent points, h and r are divided into different ranges. By contradiction, it is obtained that the h-restricted vertex diagnosability is 2n-h-4 for a range of 1≤h≤2n-7 of the alternating group graphs. Then, based on the relationship between the h-restricted vertex diagnosability and the r-restricted edge diagnosability, the r-restricted edge diagnosability is determined to be 2n-r-4 for a range of 3≤r≤2n-5 of the alternating group graphs. In addition, by constructing distinct consistent faulty pairs and proving that they are indistinguishable, the h-restricted vertex diagnosability of the alternating group graphs are determined to be 1, 0, 0 for h=2n-6, 2n-5, 2n-4, respectively, and the r-restricted edge diagnosability of the alternating group graphs are determined to be 2n-6, 2n-7 for r=1, 2, respectively. These results show the maximum number of the faulty elements that can be self-identified by the alternating group graphs under the hybrid faulty circumstance, reflecting the maximum fault diagnosis capability of the systems.