In the work we present experimental results of ac magnetization losses measurements performed in the presence of a dc-bias magnetic field. Both ac and dc magnetic fields were coaxial and directed perpendicularly to the flat surface of sample tapes. The HTS tapes used in our experiments are commercially available composite tapes, namely a BSCCO-2223/Ag multifilamentary tape and an YBCO-123 coated conductor tape. The measurements were carried out with a sinusoidally varying magnetic fields at frequency range of about 21-113 Hz, and amplitudes up to 100 mT. The superimposed a dc-bias magnetic field was of the order of up to 50 mT. At a certain magnetic field amplitude, and at a certain dc bias magnetic field, a distinguish minimum in ac losses is observed. Occurrence of the ac loss minima differs considerably for two studied sample tapes.