The abundance of molecular oxygen in dense molecular clouds is a key problem within astrochemistry. Because of its great reactivity (e.g. burning), the availability of oxygen regulates the abundances of almost all molecules. The interstellar medium is thought to be oxygen-rich (elemental C/O=0.5) and all theoretical models predict that the oxygen not locked up in CO will be in O2. However, despite sensitive searches, gaseous O2 has never been detected in the interstellar medium or in other galaxies. Hence it has been suggested that the excess O is frozen out in icy grain mantles. Since H2O ice contains typically only 10 % of the available elemental O, solid O2 is the most likely candidate. Indeed, theoretical models for the composition of icy grain mantles predict that O2 can be an important grain mantle molecule under some physical conditions. We propose high resolution spectroscopic observations with the ISO satellite towards a number of embedded sources and southern star-forming regions in order to detect the weak transition of solid molecular oxygen and the sharp transition of its photolysis product ozone. Since O2 is a homonuclear diatomic molecule, its vibration and rotation do not produce a change in dipole moment, making it IR inactive and radio quiet. Interaction with neighbour atoms in the solid state however can perturb the symmetry of the vibrations, and modes become weakly infrared active. The fundamental transition of O2 at 6.4 mu has been recently detected in the laboratory. The behaviour of solid oxygen and ozone in astrophysically relevant ice mixtures has been extensively studied at Leiden Observatory Laboratory in order to make the search for these molecules with ISO successful. For our objects which have a typical visual extinction of 20 mag, we would be able to detect the solid O2 feature if the solid O2 abundance is larger than 10 % of the elemental O. The detection of solid molecular oxygen and ozone and the estimation of their abundances represent exciting tools in infrared astronomy and may reveal if oxygen depleted on grains may account for the lack of oxygen measured in the gas phase.