Cut-off lows are closed cyclonic circulations that develop in high levels of the troposphere, separated from the westerly flow. They usually are associated with deep tropopause descent, allowing stratospheric air intrusions to the troposphere, which can lead to risks for the population, such as increments in surface ozone concentrations, increases of potential instability or generation of clear air turbulence. There is a preferential zone for the development of these systems west of South America, over the Pacific Ocean, and for this reason the goal of this paper is to progress towards understanding the behavior of the tropopause in cut-off lows that affect the south of this continent. The dynamic definition of the tropopause, based on the discontinuity in the vertical of potential vorticity was used. The tropopause was identified with three different values of this quantity: -1.6, -2 and -3 PVU. 81 cases of cut-off lows that develop west of the Andes between 1998 and 2008 were analyzed, and the tropopause drop could be quantified in each one of them. The dynamic tropopauses of the studied cut-off lows showed drops with maximum values between 650 hPa and 550 hPa, depending of the potential vorticity value selected. The position of the maximum fall, relative to the center of the systems, was also analyzed, finding a dominant preference for the equatorial sector of the cut-off lows.