Carbon and oxygen isotopic ratios are reported for a sample of 46 Mira and SRa-type variable asymptotic giant branch (AGB) stars. Vibration–rotation first and second-overtone CO lines in 1.5–2.5 μm spectra were measured to derive isotopic ratios for 12 C/13 C, 16 O/17 O, and 16 O/18 O. Comparisons with previous measurements for individual stars and with various samples of evolved stars, as available in the extant literature, are discussed. Models for solar composition AGB stars of different initial masses are used to interpret our results. We find that the majority of M-stars have main sequence masses≤ 2 M⊙ and have not experienced sizable third dredge-up (TDU) episodes. The progenitors of the four S-type stars in our sample are slightly more massive. Of the six C-stars in the sample three have clear evidence relating their origin to the occurrence of TDU. Comparisons with O-rich presolar grains from AGB stars that lived before the formation of the solar system reveal variations in the interstellar medium chemical composition. The present generation of low-mass AGB stars, as represented by our sample of long period variables (LPVs), shows a large spread of 16 O/17 O ratios, similar to that of group 1 presolar grains and in agreement with theoretical expectations for the composition of mass 1.2–2 M⊙ stars after the first dredge-up. In contrast, the 16 O/18 O ratios of present-day LPVs are definitely smaller than those of group 1 grains. This is most probably a consequence of the the decrease with time of the 16 O/18 O ratio in the interstellar medium due to the chemical evolution of the Milky Way. One star in our sample has an O composition similar to that of group 2 presolar grains originating in an AGB star undergoing extra-mixing. This may indicate that the extra-mixing process is hampered at high metallicity, or, equivalently, favored at low metallicity. Similarly to O-rich grains, no star in our sample shows evidence of hot bottom burning, which is expected for massive AGB stars.