The electron kinetics in weakly ionized helium under the action of DC and HF fields of angular frequency omega is investigated by solving the homogeneous electron Boltzmann equation using the classical two-term expansion approximation. The analysis is based on a consistent set of electron cross sections which is derived by adjusting experimental cross section data in such a way that calculated and measured electron swarm parameters are in agreement. In the case of HF fields the analysis is based on the DC effective field approximation which is valid for omega > tau e-1, where tau e is the characteristic time for electron energy relaxation by collisions with the atoms. The influence of omega on the electron energy distribution function, transport parameters, rate coefficients and fractional power transfer is investigated and a detailed comparison of the DC and HF situations is made. It is shown that for reduced effective fields in the range 10-16-10-15 V cm2, as typically found in low-pressure discharges, the mean electron kinetic properties are nearly the same in the whole range of omega > tau e-1 as for the DC case.