Unsteady components of the second-order axial velocity and temperature within a tapered pulse tube were obtained by using a hybrid method of solution. In this method, the unsteady components of the second-order axial velocity and temperature consist of an analytical solution and a numerical solution. The effects of the operating frequency and the taper angle on the unsteady components of the second-order mass flux and temperature were shown. The unsteady second-order mass flux and the time-averaged enthalpy flow by the unsteady second-order mass flux increase as the second-order displacement volume at the cold end increases. (C) 2002 Elsevier Science Ltd. All rights reserved.