The aims of this paper are: 1) to revisit the Tc content of a sample of oxygen-rich asymptotic giant branch (AGB) variables and 2) to increase the number of such stars for which the Li abundance has been measured to provide constraints on theoretical
models of extra-mixing processes. To this end, we analysed high-resolution spectra of 18 sample stars for the presence of absorption lines of Tc and Li. The abundance of the latter was determined by comparing the observed spectra to hydrostatic MARCS model spectra. Bolometric magnitudes were established from near-IR photometry and pulsation periods. We reclassify the star V441 Cyg as Tc-rich, and the unusual Mira star R Hya, as well as W Eri, as Tc-poor. The abundance of Li, or an upper limit to it, was determined for all of the sample stars. In all stars with Tc we also detected Li. Most of them have a Li content slightly below the solar photospheric value, except for V441 Cyg, which has ~1000 times the solar abundance. We also found that, similar to Tc, a lower luminosity limit seems to exist for the presence of Li. We conclude that the higher Li abundance found in the cooler and higher luminosity objects could stem from a Li production mechanism operating on the AGB. The stellar mass might have a crucial influence on this (extra-mixing) production mechanism. It was speculated that the declining pulsation period of R Hya is caused by a recent thermal pulse (TP). While not detecting Tc does not rule out a TP, it indicates that the TPs are not strong enough to drive dredge-up in R Hya. V441 Cyg, on the other hand, could either be a low-mass, intrinsic S-star that produced its large amount of Li by extra-mixing processes, or an intermediate-mass star (M>=M_sun) undergoing Li production due to hot bottom burning.
