The thermal stereomutations and [1,3] carbon sigmatropic shifts shown by (+)-(1S,2S)-trans-1-(E)-propenyl-2-methylcyclobutane and by (-)-(1S,2R)-cis-1-(E)-propenyl-2-methylcyclobutane in the gas phase at 275 degreesC leading to 3,4-dimethylcyclohexenes have been followed. The reaction-time-dependent data for concentrations and enantiomeric excess values for substrates and [1,3] shift products have been deconvoluted to afford rate constants for the discrete isomerization processes. Both trans and cis substrates react through four stereochemically distinct [1,3] carbon shift paths. For one enantiomer of the trans reactant the relative rate constants are k(si) = 58%, k(ar) = 5%, k(sr) = 33%, and k(ai) = 4%. For a single enantiomer of the cis reactant, K-si = 18%, K-ar = 11%, K-sr = 51%, and K-ai = 20%. A trans starting material reacts through orbital symmetry allowed suprafacial, inversion and antarafacial, retention paths to give trans-3,4-dimethylcyclohexenes 63% of the time. A cis isomer reacts to give the more stable trans-3,4-dimethylcyclohexenes through orbital symmetry-forbidden suprafacial, retention and antarafacial, inversion paths 71 % of the time. The [1,3] carbon sigmatropic shifts are not controlled by orbital symmetry constraints. They seem more plausible rationalized as proceeding through diradical intermediates having some conformational flexibility after formation and before encountering an exit channel. The distribution of stereochemical outcomes may well be conditioned by dynamic effects. The thermal stereomutations of the 1-(E)-propenyl-2-methylcyclobutanes take place primarily through one-center epimerizations. For the trans substrate, the relative importance of the three distinction rate constants are k(2) = 48%, k(1) = 34%, and k(12) = 18%. For the cis isomer, K-2 = 44%, K-1 = 32%, and K-12 = 24%. These patterns are reminiscent of ones determined for stereomutations in 1,2-disubstitued cyclopropanes.