The writers have studied peristaltic flow of a hyperbolic tangent fluid in a diverging tube. The flow was investigated in a wave frame of reference moving with the velocity of the wave. The governing equations of hyperbolic tangent fluid in cylindrical coordinates were modeled. Heat and mass transfer phenomena were taken into consideration. The resulting nonlinear momentum, energy, and mass equations were simplified using long wavelength and low Reynolds number approximations. The resulting problem was solved using two analytical techniques, a regular perturbation method in terms of a variant of the Weissenberg number, and a homotopy analysis method. A graphical comparison of both of the solutions is presented for velocity, temperature, and concentration profiles. The expressions for axial velocity, temperature, mass concentration, heat and mass transfer coefficients, and axial pressure gradient were obtained, and the effects of various emerging parameters on these flow characteristics are illustrated graphically. The writers graphically demonstrate the numerical results for the pressure rise and frictional force for different waveforms (sinusoidal, multi-sinusoidal, triangular, square, and trapezoidal). Trapping phenomena were taken into consideration when plotting the streamlines pattern. (C) 2013 American Society of Civil Engineers.