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The aim of this paper is to investigate the $^{17}$O/$^{18}$O ratio for asample of AGB stars, containing M-, S- and C-type stars. These ratios areevaluated in relation to fundamental stellar evolution parameters: the stellarinitial mass and pulsation period. Circumstellar $^{13}$C$^{16}$O,$^{12}$C$^{17}$O and $^{12}$C$^{18}$O line observations were obtained for asample of nine stars with various single-dish long-wavelength facilities. Lineintensity ratios are shown to relate directly to the surface $^{17}$O/$^{18}$Oabundance ratio. Stellar evolution models predict the $^{17}$O/$^{18}$O ratioto be a sensitive function of initial mass and to remain constant throughoutthe entire TP-AGB phase for stars initially less massive than 5\,$M_{\odot}$.This makes the measured ratio a probe of the initial stellar mass. Observed$^{17}$O/$^{18}$O ratios are found to be well in the range predicted by stellarevolution models that do not consider convective overshooting. From this,accurate initial mass estimates are calculated for seven sources. For theremaining two sources two mass solutions result, though with a largerprobability that the low-mass solution is the correct one. Finally, hints at apossible separation between M/S- and C-type stars when comparing the$^{17}$O/$^{18}$O ratio to the stellar pulsation period are presented.

Nucleosynthesis in AGB stars traced by oxygen isotopic ratios. I - Determining the stellar initial mass by means of the $^{17}$O/$^{18}$O ratio