The results of experimental study of the critical current and AC losses in high pressure-synthesized MgB2bulk superconductors are presented. The method is based on the use of the transformer configuration and suitable for samples in the form of hollow superconducting cylinders and rings. It was shown that the critical current measured by the transformer method is an order of magnitude lower than the value given by the magnetization technique. The obtained dependencies of the losses on current and frequency reveal the deviations from the critical state model behavior and reflect structural peculiarities of the investigated MgB2samples.