Rotational velocities of the giants in symbiotic stars: II. Are S-type symbiotics synchronized?

We have measured the projected rotational velocities (v sin i) of the mass donors for 29 S-type symbiotic stars using high resolution spectroscopic observations and the cross-correlation function (CCF) method. The results of the CCF have been controlled with synthetic spectra. The typical rotational velocity of the K and M giants in S-type symbiotics appeared to be 4.5 < vsini < 11.7 km/s. In a sub-sample of 16 S--type symbiotic stars (with known orbital periods and well measured vsini) 15 have deviations from synchronization less then the 3-sigma level. This means that we did not find evidence for a statistically significant deviation from the synchronization for any of these 15 objects. The deviation from synchronization is statistically significant (at confidence level >99%) only for the recurrent nova RS Oph. For 22 S-type symbiotics we give clues as to what their orbital periods could be.