Pressure stability in the ultrahigh vacuum (UHV) system of a gravitational wave detector is a crucial point for its sensitivity limit. We carried out an investigation in order to detect pressure fluctuations in an UHV system pumped with an ion pump. The expected characteristics of pressure pulses caused by desorption were simulated with Monte Carlo methods. Test equipment was developed with a sensitivity limit for relative pressure changes of 10(-3) at a base pressure of 10(-6) Pa in the range up to 1 kHz, and of 10(-4) below 40 Hz. Pressure fluctuations in the 10(-4) range of working pressure were found in the frequency range <40 Hz and larger pressure pulses in the percent range with a frequency of about 1 in 4 h.