The solution for the turbulent near-bottom boundary layer produced by a progressive wave train is advanced to second order in wave steepness. As in the first-order analysis (part 1) the effective viscosity is assumed to be the product of a vertical length scale and the first few Fourier components of a shear velocity based on the instantaneous, local bed shear stress. An analytical solution for the second-order flow field is obtained, with attention directed primarily toward the second-order wave-induced steady current or mass transport. The mass transport is found to depend critically on temporal variation of the effective viscosity. The most dramatic result of the analysis of a predicted reversal of the mass transport produced by relatively long waves. This result, for which supporting experimental evidence is presented, has not been predicted and cannot be obtained by a time-invariant eddy viscosity model. Implications of the present results for related problems are discussed.