We present a spectral analysis of the narrow-line Seyfert 1 galaxy I Zwicky 1, focusing on the characteristics of the ionised absorbers as observed with XMM-Newton in 2005. The soft X-ray spectrum shows absorption by two components of ionised gas with a similar column density (N_H~10^{21} cm^{-2}) and ionisation parameters logxi~0 and 2.5. Comparing this observation with a 2002 XMM-Newton data set, we see a clear anti-correlation between the X-ray ionisation parameter xi_X and the 0.1-10 keV luminosity. Viable explanations for this effect include transient clouds or filaments crossing the line of sight in a complex geometry or a gas observed in non-equilibrium. The outflow velocity of the X-ray low-ionisation absorber is consistent with the outflow of the UV absorber detected in a past Hubble Space Telescope observation. In addition, the ionic column densities of CIV and NV derived from the X-ray model are consistent with the UV values. This suggests that the low-ionisation outflowing gas may survive for many years, despite large changes in flux, and that there is a tight connection between the X-ray and UV absorbers that can only be confirmed with a simultaneous UV and X-ray observation.
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