Aphids feed on the phloem sap of their host plants. The chemical composition of this sap differs between plant species and is modulated by environmental factors. To understand why Myzus persicae (Sulzer) (Hemiptera: Aphididae) is able to infest various plant taxa, we investigated how aphids of this species respond to various sucrose-to-amino acid ratios of their diet. Moreover, we studied whether they are able to recover from periods with suboptimal nutrition. Preference and performance bioassays were performed using artificial diets with sucrose-to-amino acid ratios of 2.4:1 (optimal ‘control’ diet), 4.8:1 (‘high sucrose’), 1.2:1 (‘high amino acids’), or 1:0 (‘no amino acids’). Also, the capacity to recover from periods on suboptimal diet (i.e., the ‘no amino acids’ diet) was assessed. In four-choice assays, both nymphs and adults of M. persicae were rarely found on the ‘no amino acids’ diet and they were similarly distributed on the other diets. As long as amino acids were available, the sucrose-to-amino acid ratio had only minor effects on aphid development and reproduction. On the suboptimal diet, nymphs survived, but with almost no weight gain over time. After transfer to the ‘control’ diet, they gained weight and reproduced with only low fitness deficits compared to aphids kept on the ‘control’ diet for the whole time. The capacity to survive under suboptimal nutrition and recover from it was dependent on the length of the period on the suboptimal diet. The ability to cope with different dietary sucrose-to-amino acid ratios and to withstand suboptimal nutrition for several days may contribute to the broad host plant spectrum of M. persicae and may explain why this species is a serious pest in agricultural systems.