Nonlinear dynamics of diffusional-thermal instability in diffusion flames is numerically investigated by employing a diffusion flame established in the stagnant mixing layer as a model. Particular attention is focused on the pulsating-instability regime, which arises for Lewis numbers sufficiently greater than unity. Once the steady flame structure is obtained for a prescribed value of the initial Damkohler number, transient evolution of the flame is calculated after a finite amount of the Damkohler-number perturbation is imposed on the steady flame. Depending on whether the initial Damkohler number is greater than the bifurcation Damkohler number or not, evolution of the transient flame structures can be differently characterized. If the initial Damkohler number is smaller than the bifurcation Damkohler number, pulsating instability can be triggered without any external perturbations, while if the initial Damkohler number is greater than the bifurcation Damkohler number, flame oscillations can be amplified only for the perturbed Damkohler number smaller than the threshold Damkohler number. Therefore. character of the nonlinear instability is subcritical. Once the oscillation amplitudes grow too large, flames are eventually led to extinction. Locus of the threshold Damkohler number is presented, which could be used as a revised extinction criterion for diffusion-flamelet library in the laminar flamelet regime of turbulent combustion.