Particle densities of helium atoms in the ground and excited states have been calculated for non-L.T.E. plasmas on the basis of a collisional-radiative model in which singlet and triplet states have separately been taken into account. Distinction is made between two physical situations: 1- a homogeneous stationary state, 2- a transient and/or inhomogeneous plasma state. In both cases, the particle densities have been calculated for an optically thin, a slightly optically thick and strongly absorbing plasmas. Only the results for the homogeneous stationary state are presented in this paper. Those for the transient and/or inhomogeneous states have been summarized in numerical tables which will be sent on request. (Title: "Tables of reduced population coefficients for the levels of atomic helium", Report EUR-CEA-FC-697.) The tables are sufficiently complete to permit a wide application in the field of spectroscopic diagnostics of different types of non-L.T.E. plasmas. - Comparison of our results with the values measured by Boersch et al. 10 shows good agreement with our calculations when one assumes that the observed plasma is strongly inhomogeneous and dominated by diffusion.