An experimental study of heat transfer characteristics near the critical pressure has been performed with an internally-heated vertical annular channel cooled by R-134a fluid. Two series of tests have been completed: (a) steady-state critical heat flux (CHF) tests, and (b) heat transfer tests for pressure reduction transients through the critical pressure. In the present experimental range, the steady-state CHF decreases with increase of the system pressure for fixed inlet mass flux and subcooling. The CHF falls sharply at about 3.8 MPa and shows a trend towards converging to zero as the pressure approaches the critical point of 4.059 MPa. The CHF phenomenon near the critical pressure does not lead to an abrupt temperature rise of the heated wall, because the CHF occurs at remarkably low power levels. In the pressure reduction transients, as soon as the pressure passes below the critical pressure from the supercritical pressure, the wall temperatures rise rapidly up to very high values due to the departure from nucleate boiling. The wall temperature reaches a maximum at the saturation point of the outlet temperature, and then tends to decrease gradually.