Systems’ essential dynamics over finite time are referred to as transient dynamics. They are thought to be more relevant to physically observed dynamical behaviors. In this talk, we are mainly concerned about long transient dynamics in stochastic systems. In particular, we consider two different models with small noise perturbation arising from population dynamics, where species only coexist over a long finite time period and go to extinction in the long run. To capture such transient persistent dynamics, we use quasi-stationary distributions (QSDs) and study their noise-vanishing asymptotic. Since QSD is closely related to the spectrum of the Fokker-Planck operator, our method is mainly based on PDE analysis. It is worthwhile to mention that the second-order coefficients of the Fokker-Planck operator are degenerate on the boundary for any fixed noise and vanish in the zero-noise limit, resulting in essential technical difficulties. In the end of the talk, I would list some topics for future work.