[en] In a paper with a similar title, Yamanaka has calculated the mass polarization effect (to first order in μ/M) for several low-lying states of the two-electron atoms and ions with atomic number Z from 2 to 10. Here we improve the previous results by using Hylleraas variational wavefunctions with up to 560 terms and extend the calculation to include some additional states and the Z = 1 ground state. In addition, we compute the second-order effect using the method of pseudostate summation. A nonperturbative method of computation is also discussed and used as a check