Cells within solid tumours can become deprived of nutrients; in order to survive, they need to invoke mechanisms to conserve these resources. Using cancer cells in culture in the absence of key nutrients, we have explored the roles of two potential survival mechanisms, autophagy and elongation factor 2 kinase (eEF2K), which, when activated, inhibits the resource-intensive elongation stage of protein synthesis. Both processes are regulated through the nutrient-sensitive AMP-activated protein kinase and mechanistic target of rapamycin complex 1 signalling pathways. We find that disabling both autophagy and eEF2K strongly compromises the survival of nutrient-deprived lung and breast cancer cells, whereas, for example, knocking out eEF2K alone has little effect. Contrary to some earlier reports, we find no evidence that eEF2K regulates autophagy. Unexpectedly, eEF2K does not facilitate survival of prostate cancer PC3 cells. Thus, eEF2K and autophagy enable survival of certain cell-types in a mutually complementary manner. To explore this further, we generated, by selection, cells which were able to survive nutrient starvation even when autophagy and eEF2K were disabled. Proteome profiling using mass spectrometry revealed that these ‘resistant’ cells showed lower levels of diverse proteins which are required for energy-consuming processes such as protein and fatty acid synthesis, although different clones of ‘resistant cells’ appear to adapt in dissimilar ways. Our data provide further information of the ways that human cells cope with nutrient limitation and to understanding of the utility of eEF2K as a potential target in oncology.