The study of symbiotic systems is of considerable importance in our understanding of binary system stellar evolution in systems where mass-loss or transfer takes place. Elemental abundances are of special significance since they can be used to track mass exchange. However, there are few symbiotic giants for which the abundances are fairly well determined. Here, we present for the first time a detailed analysis of the chemical composition for the giants in the RW Hya and SY Mus systems. The analysis is based on high-resolution (R similar to 50 000), high signal-to-noise (S/N), near-IR spectra. Spectrum synthesis employing standard local thermal equilibrium (LTE) analysis and atmosphere models was used to obtain photospheric abundances of CNO and elements around the iron peak (Sc, Ti, Fe, and Ni). Our analysis reveals a significantly sub-solar metallicity, [Fe/H] similar to -0.75, for the RW Hya giant confirming its membership in the Galactic halo population and a near-solar metallicity for the SY Mus giant. The very low C-12/C-13 isotopic ratios, similar to 6-10, derived for both objects indicate that the giants have experienced the first dredge-up.