We present multi-frequency radio continuum as well as HI observations of the composite galaxy NGC6764, which has a young, circumnuclear starburst and also harbours an active galactic nucleus (AGN). These observations have been made at a number of frequencies ranging from ~600 MHz to 15 GHz using both the GMRT and the VLA. They reveal the structure of the bipolar bubbles of non-thermal, radio emission which are along the minor axis of the galaxy and extend up to ~1.1 and 1.5 kpc on the northern and southern sides respectively. Features in the radio bubbles appear to overlap with filaments of H_alpha emission. The high-resolution observations reveal a compact source, likely to be associated with the nucleus of the galaxy, and a possible radio jet towards the south-west. We have compiled a representative sample of galaxies with bubbles of non-thermal radio emission and find that these are found in galaxies with an AGN. The HI observations with the GMRT show two peaks of emission on both ends of the stellar-bar and depletion of HI in the central region of the galaxy. We also detect HI in absorption against the central radio peak at the systemic velocity of the galaxy. The HI-absorption spectrum also suggests a possible weak absorption feature blue-shifted by ~120 km/s, which requires confirmation. A similar feature has also been reported from observations of CO in emission, suggesting that the circumnuclear starburst and nuclear activity affect the kinematics of the atomic and molecular gas components, in addition to the ionised gas seen in H_alpha and [N II].