Low-pressure proportional counters (LPPCs) with walls made from the elements C, Mg, Al, Si, Fe and Zr and from the chemical compounds A-150 plastic, AlN, Al2O3, SiO2 and ZrO2 were used to measure neutron fluence-to-kerma conversion coefficients at energies up to 66 MeV. The LPPCs served to measure the absorbed dose deposited in the gas of a cavity surrounded by the counter walls that could be converted to the absorbed dose to the wall on the basis of the Bragg-Gray cavity theory. Numerically the absorbed doses to the walls were almost equal to the corresponding kerma values of the wall materials. The neutron fluence was determined by various experimental methods based on the reference cross sections of the 1H(n, p) scattering and/or the 238U(n, f) reactions. The measurements were performed in monoenergetic neutron fields of energies of 5 MeV, 8 MeV, 15 MeV and 17 MeV and in polyenergetic neutron beams with prominent peaks of energies of 34 MeV, 44 MeV and 66 MeV. For the measurements in the polyenergetic neutron beams, significant corrections for the contributions of the non peak energy neutrons were applied. The fluence-to kerma conversion coefficients of N and O were determined using the difference technique applied with matched pairs of LPPCs made from a chemical compound and a pure element. This paper reports experimental fluence-to-kerma conversion coefficient values of eight elements and four compounds measured for seven neutron energies, and presents a comparison with data from previous measurements and theoretical predictions. The distributions of the absorbed dose as a function of the lineal energy were measured for monoenergetic neutrons or, for polyenergetic neutron fields, deduced by applying iterative unfolding procedures in order to subtract the contributions from non-peak energy neutrons. The dose distributions provide insight into the neutron interaction processes.