Empirical evidence suggests that carry-over effects (COEs) can have a strong influence on the time evolution of populations. Here, COEs are defined as any event or process in one season that affects individual performance in a non-lethal manner during the following seasons. Our results have the potential to explain previously reported experimental results and to provide new biological phenomena. The population response to COEs is typically considerably more complicated than previously believed. We found that COEs that reduce the reproduction rates always decrease the population density. However, in the case of COEs that reduce the survival rates, there could be an increase in the population size. Regarding the dynamical behaviour, the impact of COEs is primarily associated with a stabilizing role in ecological research. However, this response is guaranteed only in COEs affecting the reproduction rate when the survival is density independent (or has a negligible density-dependent component). Interestingly, COEs have the potential to create bi-stability scenarios, particularly in COEs across multiple seasons.