  We have measured the rotational velocities (v.sini) of the mass donors in a
number of D'--type symbiotic stars, using the cross-correlation function
method. Four from five D' symbiotic stars with known v.sini, appeared to be
very fast rotators compared with the catalogues of v.sini for the corresponding
spectral types. At least three of these stars rotate at a substantial fraction
(>=0.5) of the critical velocity. This means that at least in D'-type
symbiotics the cool components rotate faster than isolated giants. If these
binary stars are synchronized, their orbital periods should be relatively short
(4-60 days). We also briefly discuss the possible origin of the rapid rotation
and its connection with mass loss and dust formation.
