High resolution spectra containing the Mg II h and k resonance doublet have been obtained using the long wavelength spectrometer of IUE, for 7 late-type stars (F0 to G8). In one of these stars, β Hyi, two sharp absorption features were detected against the chromospheric emission cores. Using the study of Crutcher (1982) the authors can employ the velocity of one of these features to identify it as arising from the local interstellar medium (LISM), while the other feature appears due to chromospheric self-absorption. Although the other stars do not show separate intrinsic and LISM features it is possible to use evidence both from wavelength shifts and line half-widths to identify the interstellar absorption components. This gives the Mg II column densities along the lines of sight to five of these stars and upper limits towards the other two.