Low-molecular-weight ('volatile') radiolysis products of low-density polyethylene (LDPE) and polypropylene (PP) films were investigated by thermal desorption-(TDS)-GC-MS after absorbed doses of up to 25 kGy. The films produce fingerprint chromatograms with highly characteristic patterns of groups of radiation-induced peaks; these are mainly hydrocarbons, aldehydes, ketones, and carboxylic acids with concentrations (after 25 kGy) ca one order of magnitude below that of the residual hydrocarbons (oligomers). PP additionally produces very substantial amounts of three degradation products of phenol-type antioxidants. The low molecular-weight (MW) radiolysis products are retained for considerable times in LDPE films and they are retained in PP films much longer than had been expected. Besides product identification, the following topics are addressed: Effects of the absorbed dose and the desorption temperature; comparison of several commercial (proprietary) films; high-temperature thermal desorption; the question whether TDS analyzes radiation-induced artifacts rather than genuine products; the possible existence of cyclic radiolysis products; the possibility of identifying an LDPE film as irradiated after a dose of only 1 kGy; and atypical trace fragments of antioxidants. Finally, the geometry and efficiency of the thermal desorption system is briefly discussed, and the implications of our findings for irradiation detection and for the safety of irradiated materials are considered.