Cavitation instabilities such as rotating cavitation and cavitation surge often occur in high speed turbopumps. It has been shown by a stability analysis that the cause of cavitation instabilities is well explained by the positive mass flow gain factor which means the increase of cavity volume against the decrease(increase)of flow rate(angle of attack). The cavitation compliance which means the increase of cavity volume in response to the decrease of inlet pressure is responsible for the frequency of instabilities. However, the onset condition prediction often fails when the quasi-steady assumption is applied in 1-D stability analysis of cavitation surge. In the present study, unsteady characteristics, i.e. the phase lag in the response of cavity volume against the flow rate / inlet pressure fluctuations, are taken into account in a stability analysis of cavitation surge in the form of the first order lag elements. The onset criteria considering the time lag is newly proposed for 1-D stability analysis, and the criteria is validated by comparisons with a 2-D stability analysis based on a singularity method applied to a free streamline theory.