We propose to observe selected Cepheids in the Large Magellanic Cloud (LMC) using the IRAS 12 micron band. Using our previously established period-luminosity relation (PLR) at 12 microns for galactic Cepheids, we will derive a new and independent distance measurement for the LMC. These ISO Cepheid observations will also enable us to determine a new 12 micron PLR for the LMC Cepheids. This will allow us to compare the galactic PLR with a PLR determined for Cepheids in an extragalactic system. We will then search for systematic differences between these two relationships. This comparison will be significant since the LMC is known to be somewhat metal poor in comparison to the Milky Way galaxy. The PLR at the far-infrared wavelength of 12 microns effectively provides us with a new and powerful technique for determining galactic and extragalactic distances. Because of the diminished amplitude and diminished asymmetry of the light variation for Cepheids in the infrared, reliable determinations of mean light levels are possible by employing a simple mean of several random- phase observations. Furthermore, at a wavelength of 12 microns the interstellar dust produces no measurable effects, so uncertain corrections for interstellar extinction are not required. Finally, the absence of metallic absorption features in this part of the spectrum should minimize any systematic effects due to chemical abundances. The observations we propose will enable us to demonstrate the power and the reliability of this new technique for determining galactic and extragalactic distances. This technique requires minimal observations and is independent of interstellar extinction and differences in chemical composition. The results from this proposal will be essential for studies of galactic structure and the local extragalactic distance scale which use data from IRAS, ISO, and SIRTF.