Anthracene was used as a chemical probe to evaluate hydrogen donating abilities (HDAs) of two petroleum vacuum residues and their SARA fractions (i.e., saturates, aromatics, resins, and asphaltenes), and hydrogen donating kinetics of aromatics and resins were then analyzed. Also, 9,10-dihydroanthracene was used as a chemical probe to evaluate hydrogen accepting abilities of the asphaltenes of the residues. Coking propensities of both residues under thermal processing at 400 °C were evaluated by their coke induction periods. Results show that HDA of either residue proceeds to increase at first and then tends to decline under thermal processing, forming a maximum in the middle. The HDA peak value increases progressively with temperature increasing; the two residues may exhibit either different or similar HDAs at certain test conditions. When the four SARA fractions coexist in the form of a residue for further thermal processing, there exhibits synergism in HDA among the four SARA fractions. Hydrogen donating of aromatics and resins can be treated by first-order kinetics, and both rate constant and initial rate in hydrogen donating for resins show much higher values than those for aromatics. Asphaltenes accept substantially more hydrogens than the amounts they donate. A comprehensive analysis of the data thus obtained shows hydrogen transfer among the SARA fractions is essentially related to coking propensity of residue under thermal processing, where asphaltenes accept hydrogens from resins in the immediate neighborhood that are then supplemented by aromatics. Donatable hydrogens in asphaltenes alone appear insufficient to prevent asphaltenic radicals from combining to form coke. A residue whose asphaltenes accept more hydrogens with resins and aromatics releasing fewer hydrogens exhibits a higher coking propensity under thermal processing. Hydrogen donor/acceptor additives may serve to suppress/promote coke formation by influencing the coking rates of asphaltenes in the center by supplementing/depleting donatable hydrogens of the surrounding medium constituents, that is, resins and aromatics.