The Target of Rapamycin (TOR) signalling network plays important roles in aging and disease. The AMP-activated protein kinase (AMPK) and the Gsk3 kinase inhibit TOR during stress. We performed genetic interaction screens using synthetic genetic arrays (SGA) with gsk3 and amk2 as query mutants, the latter encoding the regulatory subunit of AMPK. We identified 69 negative and 82 positive common genetic interactors, with functions related to cellular growth and stress. The 120 gsk3-specific negative interactors included genes functioning in translation and ribosomes. The 215 amk2-specific negative interactors included genes functioning in chromatin silencing and DNA damage repair. Both amk2- and gsk3-specific interactors were enriched in phenotype categories related to abnormal cell size and shape. We also performed SGA screen with the amk2 gsk3 double mutant as a query. Mutants sensitive to 5-fluorouracil, an anticancer drug are under-represented within the 305 positive interactors specific for the amk2 gsk3 query. The triple-mutant SGA screen showed higher number of negative interactions than the double mutant SGA screens and uncovered additional genetic network information. These results reveal common and specialized roles of AMPK and Gsk3 in mediating TOR-dependent processes, indicating that AMPK and Gsk3 act in parallel to inhibit TOR function in fission yeast.