Following the studies of Moen et at. [1986], Shepherd [1986], and Lee [1991, 1993], regarding the dependence of some dynamic parameters of detonation on the "detonation instability," the present work has been performed to investigate the role of "detonations instability" on the direct initiation problem. This study has been carried out by numerical integration of the one-dimensional Euler equations in aplanar geometry. For the chemical kinetics model, asingle-step Arrhenius law was assumed. The present results show that initiation process has the same mechanism for both stable and unstable detonations. It is shown that the ZND induction length is not an appropriate length scale to specify the highly transient processes in the so-called quasi-steady period. However, for unstable detonations when the activation energy is very high, no unique value can be defined for the critical initiation energy. It was found that analytical models based on the Zeldovich criterion cannot predict the critical initiation energy over the full range of activation energies considered in this study. This is because the Zeldovich criterion does not consider any dynamic effects during the quasi steady period.