In Daphnia-algal systems, the effect of nutrient enrichment on stability is an important ecological issue. Here I consider a system of Daphnia and two potential prey; one prey termed primary algae, which are preferentially consumed, and the other secondary algae, which yield less nutrition and are more resistant to the grazer. The presence of secondary algae is a key to the stability, but their nutritional value has not been clearly defined in the previous theory and the actual value varies. Here I use a simple mathematical model defining explicitly the nutritional values of algae and examine the stability of the systems as a function of phosphorus enrichment. Whether or not all three species can stably coexist depended on the combination of the algal species used for simulation. In systems where all the species coexist in a stable manner, in which enrichment does not necessarily lead to destabilization, there is always a critical nutritional value of the secondary algae. Empirical work supports the possibility that the unknown nutritional value of secondary algae takes a value close to the critical one. Furthermore, at the critical nutritional value, the population response in the systems to enrichment is consistent with the observed trend in natural systems. This suggests that Daphnia-algal systems in nature can maintain stability in the face of enrichment, without requiring specific assumptions such as spatial heterogeneity.