2-(2'-Hydroxyphenyl)benzoxazole (HBO) and its meta-methyl derivative (m-MeHBO) can exist in two tautomeric forms, an enol tautomer (E) and a keto tautomer (K). The stable ground state is an enol stare, E-1, and the lowest excited singlet state is a keto state, K-1*. Intersystem crossing K-1*-->K-3* is followed by tripler-state tautomerization (TST) K-3*-->E-3* if the energy relation E(K-3*) - E(E-3*) = hcx > 0 holds. In an alkane glass, the wavenumber x is >0 for approximate to 90% of all HBO molecules and for virtually all m-MeHBO molecules. The kinetics of TST of HBO, m-MeHBO and of the deuteriooxy analogues DBO and m-MeDBO in an alkane glass was studied between approximate to 2 and approximate to 80 K. TST can be observed by measuring the transient absorption after pulsed excitation, due to the different absorption spectra of K-3* and E-3*. The basic results are: (1) TST is a tunnel reaction and its kinetics is independent of temperature between 2 and 25 K, (2) The rate constant k(KE) of TST depends on the energy difference hcx. Due to the wide distribution of x, the kinetics of TST is multiexponential; an empirical biexponential description of TST yields the ratios k(1)/k(2) approximate to 5 for the rate constants and A(1)/A(2) approximate to 2 for the preexponential factors. (3) The wide distribution of the rate constant k(KE) can be rationalized by a kinetic model, in which the generation of phonons is an important rate-limiting factor. (4) The TST of DBO is approximate to 1700 times slower than that of HBO, and the TST of m-MeDBO is approximate to 700 times slower than that of m-MeHBO. - Clear glassy solutions without cracks were obtained by using absorption cells made of polymethylmethacrylate (PMMA), whose thermal expansion coefficient is similar to that of hydrocarbon glasses.