Abstract: The high-spin structure of the nucleus Pd-104 was studied through the Zr-96(C-13,5n) reaction at incident energies of 51 and 58MeV, using the Euroball IV gamma-ray spectrometer in conjunction with the DIAMANT charged-particle array. Several new medium- and high-spin bands were revealed. The already known positive-parity yrast and the negative-parity cascades were extended up to E-x similar to 13, similar to 11, and similar to 9 MeV with I-pi = (26(+)), I-pi = (23(-)), and (20(-)), respectively. The deduced band structures were compared with Woods-Saxon total Routhian surface (TRS) calculations. In addition, non-yrast low-lying positive-parity bands were identified, which were assigned to soft gamma-vibrational excitations.