Two novel neutron-based analytical techniques have been treated in this thesis, Neutron Resonance Capture Analysis (NRCA), employing a pulsed neutron source, and Neutron Incoherent Scattering (NIS), making use of a cold neutron source. With the NRCA method isotopes are identified by the isotopic-specific resonances observed in the neutron capture cross section. The capture events are detected through the prompt-gamma emissions occurring after capture, and the neutron energy at which they occur is determined with the Time of Flight (TOF) method. NRCA was improved to allow for various practical applications, i.e. 1) determination of chlorine in marble matrixes, 2) determination of the calcium to phosphorus ratio in bone, 3) determination of tin isotopes in hydroxyapatite matrixes and 4) determination of lead in bronze archaeological artefacts. The main issue was quenching the background. This was done by a combination of various expedients: 1) detector shielding, 2) detector material choice, 3) flight path length, 4) selection of gamma energies during data analysis. In NIS the measured hydrogen scattering cross section is employed to determine small hydrogen concentrations in technologically important materials. Early papers regarded the neutron scattering as isotropic and measurements were performed at one scattering angle only. However, the hydrogen scattering cross section is known to depend on hydrogen chemical binding, as expressed in the hydrogen atom's effective mass, and on the thermal motions of the hydrogen atoms in the sample, i.e. sample temperature. Both affect the anisotropy of the incoherent scattering and therefore bias the results. The goal of the research described was to increase the understanding of the NIS method and possibly render it applicable to a variety of hydrogen-containing samples. This was done by measuring at two angles and analysing the data with the aid of Monte Carlo simulations based on a more complex model, i.e. the free-gas model, that accounts for the scattering cross section dependence on hydrogen effective mass and temperature. NIS was performed both on titanium alloy samples loaded with varying hydrogen concentrations and on hydrating cement pastes. XRD (X-Ray Diffraction), MuSR (Muon Spin Resonance) and isothermal calorimetry were employed as supporting techniques for data interpretation.