We present the measurements of gas and stellar velocity dispersions in 17 circumnuclear star-forming regions (CNSFRs) and the nuclei of three barred spiral galaxies: NGC2903, NGC3310 and NGC3351 from high dispersion spectra. The stellar dispersions have been obtained from the CaII triplet (CaT) lines at 8494, 8542, 8662A, while the gas velocity dispersions have been measured by Gaussian fits to the Hbeta and to the [OIII]5007A lines. The CNSFRs, with sizes of about 100 to 150pc in diameter, are seen to be composed of several individual star clusters with sizes between 1.5 and 6.2pc on HST images. Using the stellar velocity dispersions, we have derived dynamical masses for the entire star-forming complexes and for the individual star clusters. Values of the stellar velocity dispersions are between 31 and 73 km/s. Dynamical masses for the whole CNSFRs are between 4.9x10^6 and 1.9x10^8 Mo and between 1.4x10^6 and 1.1x10^7 Mo for the individual star clusters. We have found indications for the presence of two different kinematical components in the ionized gas of the regions. The narrow component of the two-component Gaussian fits seem to have a relatively constant value for all the studied CNSFRs, with estimated values close to 25 km/s. This narrow component could be identified with ionized gas in a rotating disc, while the stars and the fraction of the gas (responsible for the broad component) related to the star-forming regions would be mostly supported by dynamical pressure.