The ruthenium(VIII) oxidation reaction has been employed to determine the distribution of alkyl groups that are bonded to aromatic structural elements in lignin and the Argonne Premium Coals. The lignin, as expected, has few aromatic methyl groups, 0.02 per 100 carbon atoms. The results for the coals, Beulah-Zap 0.86, Wyodak 1.16, Illinois No. 6 1.76, Blind Canyon 2.45, Pittsburgh No. 8 2.05, Lewiston-Stockton 2.39, Upper Freeport 2.09, and Pocahontas No. 3 7.28 methyl groups per 100 carbon atoms, exhibit a steeply stepped discontinuous rank dependence. The abundances of the other small alkyl groups, which are least prevalent in the lignin and the low-rank coals, range from about 0.2 ethyl and 0.05 propyl groups to about 0.01 butyl groups per 100 carbon atoms in the bituminous coals. The curious rank dependence for the methyl group abundances may be the consequence of major structural changes that accompany the transformation of a medium-volatile bituminous coal into a low-volatile bituminous coal. The chemical origins of the methane that is formed during the pyrolytic decomposition of these fossil materials are discussed. The analysis suggests that methane, the major portion of which is obtained at high temperature after ethane and the other simple hydrocarbons have formed and the paraffinic and hydroaromatic fragments have decomposed, is not produced predominantly from the structural elements that exist in the unreacted coal through conventional processes such as beta scission and ipso substitution. The methane that is formed at higher temperatures is accompanied by even greater molecular quantities of dihydrogen. The observations suggest that methane is produced by three reaction sequences involving oxidative condensation, hydrogen atom addition reactions that produce reactive hydroaromatic compounds, and carbene chemistry that provides a pathway to convert simple aromatic structures into methylated cyclopentane derivatives.