Strange behavior has been noticed in pressure buildup curves for gas wells producing from very low permeability, high drawdown formations. The typical unit slope on a log-log graph of real gas pseudopressure m(p) vs time for wellbore storage-dominated data becomes very steep (greater than unity) before going through a transition to the semilog straight line. A study of this behavior was made by means of a one-dimensional radial mathematical model wherein wellbore storage is treated rigorously. It was detected that buildup cases characterized by moderate to high pressure drawdown before shut-in always exhibit a shift of the conventional log-log graph to a larger value of the dimensionless wellbore storage constant, compared to the liquid solution. The typical unit slope in the wellbore storage control period is still preserved, and after that period, the buildup curve coincides smoothly with the constant physical properties liquid case. In extreme pressure drawdown cases, in addition, a more significant shift is also followed by a steepening towards the liquid solution.