SCIENTIFIC ABSTRACT In order to investigate the low-mass star-formation in molecular clouds one needs both surveys of large areas to about 10 times the sensitivity of IRAS - which is the topic of another proposal - and deep surveys of a limited number of selected regions. Large area surveys will yield complete samples of stellar populations in dark clouds, while deep surveys can be used in attempts to extend the infrared luminosity function (LF) to much lower luminosities. The present proposal thus aims at a deep search for low- luminosity young stars in a sample of nearby dense molecular cores with and without known star-formation. It is obviously important to use the same filters (LW2 and LW3) as for the large survey, but in order to avoid source confusion we judge that the 3 arcsec. pixel field of view should be used. This however means that only a very small fraction of the large survey can be covered by this deep survey and we find it natural to favour the densest and/or clustered parts of the regions. With an integration time of 0.5 hour, objects with luminosities in the range a few x 0.0001 - a few x 0.02 L-sun should be detectable, the actual luminosity limit being dependent on the steepness of the energy distributions. OBSERVATION SUMMARY As we expect the fields to contain many point sources in addition to extended emission the beam shift method (AOT = CAM03) should be the most efficient. The exact position of the reference field is a trade-off between the wish to get a clean region and the risk of increasing differential background for larger shifts (and the increased slew time). In most cases we judge that a shift equal to one or two frames should suffice.The unit integration time of 10 sec. and a total time on the target of 0.5 hours gives, according to the "time calculator", S/N = 3 for 0.06 mJy in the LW2 filter and for 0.130 mJy in the LW3. For each region we propose to concatenate the observations in the two filters in order to save some slewing time.