A highly sensitive determination of spallogenic (53)Mn (T = 2 x 106 yr) was accomplished in 0.99 g of lunar soil. The chemical yield of Mn is determined with "carrier-free" (52)Mn tracer. During a 23-day reactor irradiation the (53)Mn is transformed into (54)Mn (T = 300 days). Appropriate chemical recycling was done by ion exchange and distillation. Interferences of the (n,p) and the (n,2n) nuclear reactions were carefully studied. A (53)Mn disintegration rate of 30.3 +/- 5.5 dpm/kg results. This extremely economic method is proposed for further detailed lunar profile measurements. The Re content, which is of possible cosmochemical interest, was determined to be 11 ppb. Appropriate separation techniques were used. The rather weak and complex thermoluminescence properties made a more basic study advisable. Thermogravimetric analysis, mass spectroscopy, and Moessbauer spectroscopy were applied. The presence of ilmenite, metallic Fe etc., and of an unidentified Fe(2+)-containing compound was deduced. Natural thermoluminescence could not be proved with certainty in our surface sample. However, the complexity of the artificial thermoluminescence demands better defined mineral fractions. The fission track method was used to measure U distribution in glass spherules etc.