  We outline a non-perturbative procedure for calculating the total
photoionization cross-section of two-electron atomic systems. The procedure is
based on the Floquet-Fourie representation of the solution of the
time-dependent Schrodinger equation. The Floquet-Fourie ansatz produces a set
of equations which is recast into a generalized eigenvalue problem by means of
the complex rotation procedure. With the use of the Hylleraas-type basis
functions, the total photoionization cross-sections are obtained within the
accuracy of a fraction of a percent. The total photoionization cross-sections
for neutral helium are in good agreement with the convergent close-coupling
calculations of Kheifets and Bray [Phys. Rev. A {\bf 58}, 4501 (1999)] but
deviate notably from the experimental data of Samson {\em et al.} [J. Phys. B
{\bf 27} 887 (1994)].
